Questions on Geometry: Pythagorean theorem answered by real tutors!

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Question 1177212: The hypotenuse of a right triangle is three less than twice the shorter leg. The length of the other leg is three more than the shorter leg find the length of the shorter leg
Click here to see answer by MathLover1(20849)

Question 1178285: The roof of the building shown below has a span of 48 feet. the rafters upon which the roof is laid are 30 feet long, including a 4 foot overhung.
a. knowing that the pitch of a roof is the ratio of the rise to the run, find the pitch of this roof.
B. if the entire roofline measures 100 feet from end to end, find the total area of the roof.
c. find the percent of the roof used for the overhang
Click here to see answer by Solver92311(821)

Question 1178684: Henry got his kite stuck in a tree 13 feet above the ground. If he is standing 4 feet from the base of the tree, how far is the kite from Henry?
Click here to see answer by Alan3354(69443)

Question 1179166: Given that sec θ = 5/4 and tan θ < 0 , find the value of sin(2θ).
Click here to see answer by amarjeeth123(569)

Question 1179524: Find all primary solutions (0 ≤ x < 2π) of the equation 2sin^2(x) + 3 cos(x)=3
Click here to see answer by Edwin McCravy(20054)

Question 1180335: The foot of the ladder is sit 6 feet away from the side of the house. The top of the ladder is 8 feet up along the wall. How many feet did James adjust just a ladder to
Click here to see answer by ikleyn(52780)

Question 1180381: Find AB if DC = 5 and XY = 8

Click here to see answer by mananth(16946)

Question 1180383: A 12-meter ladder leans against a house reaching 8 meters above the ground. How far is the foot of the ladder to the foot of the house?
Click here to see answer by ikleyn(52780)

Question 1181168: Solve the following problems applying the appropriate special right triangle theorem.
1. You need as a square shaped plastic cover to be installed in front of your store as protection from COVID-19. If the length of the diagonal of your store window measure 2.8 meters, about how many square meters of plastic cover would you need?
2. Alas! There's a new shape of a pizza! It's a triangular in shape where each side measure 12 inches long. If you cut it into two equal parts, what must be the length of the edge where the pizza is sliced?@
Click here to see answer by greenestamps(13200)

Question 1181317: Frances and Joyce decided to take a shortcut through the woods to go to their friend's house. When they went home they decided to take the long way around the woods to avoid getting muddy shoes. If the length of the shortcut is equal to the square root of the sum of the squares of the other two sides, what total distance did they walk?

Click here to see answer by greenestamps(13200)

Question 1181784: I have a right angled triangle whose opposite and adjacent sides are given. Opposite side is 7 and the Adjacent side is 24. Find the six trigonometric ratios of the angle.
Click here to see answer by Boreal(15235)

Question 1181911: The equation below comes from a formula that Euclid discovered while studying right triangles.
(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2
Prove that the equation is true.(hint: try using a difference of squares)
Click here to see answer by MathLover1(20849)

Question 1182028: In ∆ACS, AC = 12, SA = 8 and SC = 16. Determine the measures of all the interior angles of the triangle.
Click here to see answer by ikleyn(52780)

Question 1182037: Sorry looked for the Similar triangle section hope this is right
Rina lives in an apartment building that is 800 m high. The building casts a shadow that is 900 m long. The shadow of the neighbouring apartment building is 1200 m long. Find the height of the neighbouring building, to the nearest metre using similar triangles.
Click here to see answer by ikleyn(52780)

Question 1182225: Can the converse of the Pythagorean theorem determine which triangle with the given three side lengths is a right triangle.
16,21,24
4,9,12
20,21,29
5,12,14
Click here to see answer by mananth(16946)

Question 1182218: A man 1.5 m tall is on the top of a building .He observes a car on the road at an angle of 75°.if the building is 30 m high ,how far is the car from the building?

Click here to see answer by mananth(16946)

Question 1182265: The height of a coconut tree is 6 m and a distance from a tree to a point in the front of the coconut tree is 12 m what is the angle of elevation of a tree?
Click here to see answer by math_tutor2020(3816)

Question 1182312: A man, 1.5m tall, is on top of the building. He observes a car on the road at an angle of 75°. If the buildibg is 30m high, how far is the car from the building?

Click here to see answer by josgarithmetic(39617)

Question 1182512: Answer the following accordingly.
1.state the law of sines.
2.in which cases,can we use the law of sines?
3.can you site real life application of law of sines? Describe how you can apply the law of sines in that situation.Give at least two situations.

Click here to see answer by josgarithmetic(39617)

Question 1182511: Applying the law of sines,solve the following problems.Round to the nearest hundredth.
1.Solve triangle MNP where N=125°,P=35 and m=12.
2.Solve triangle ABC if A=63°,a=39,and b=42.
3.Solve triangle EFG given E=35°,e=16,and f=10.
Click here to see answer by josgarithmetic(39617)

Question 1182989: The hypotenuse of right triangle is 15mc. One of the legs is 3cm more than the other. Find the length of the two legs.

Click here to see answer by amarjeeth123(569)

Question 1183355: how can I find the Geometric mean between the numbers 3 and 27

Click here to see answer by josgarithmetic(39617)

Question 1183355: how can I find the Geometric mean between the numbers 3 and 27

Click here to see answer by ikleyn(52780)

Question 1183355: how can I find the Geometric mean between the numbers 3 and 27

Click here to see answer by MathLover1(20849)

Question 1182677: A force of 100N acting horizontally to the right is to be combined with another force P acting upward to the right at an angle of 15 degrees with the vertical. If the resultant force of these two forces is 122.83N, solve force P.

-> Is it possible to use phytagorean theorem? I'm having a hard time understanding the problem. Please help..
Click here to see answer by robertb(5830)

Question 1184135: Find the length of the leg
x
. Enter the value rounded to one decimal place.

Click here to see answer by ikleyn(52780)

Question 1184136: A 15 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 5 feet from the base of the tree. The base of the tree and the ground form a right angle as shown.
What is the distance, in feet, between the ground and the top of the ladder?
Round your answer to the nearest tenth.
Click here to see answer by ikleyn(52780)

Question 1184137: The length of a rectangle is eight more than triple the width. If the perimeter is 144 inches, find the dimensions.
The width is inches.
The length is inches.

Click here to see answer by ikleyn(52780)

Question 1185773: The perimeters of two 30-60-90 triangles are in the ratio 1:2. If the hypotenuse of the larger triangle is 12, find the sides of the smaller triangle
Click here to see answer by Theo(13342)

Question 1185772: Suppose you have a 13-foot ladder and want to reach a height of 12 feet to clean out the gutters on your house. How far from the base of the house should the base of the ladder be?
Click here to see answer by greenestamps(13200)

Question 1185771: The acute angles of a right triangle have degree measures 30 and 60. If the side opposite the 60-degree angle has length 18, then what is the length of the side opposite the 30-degree angle?
Click here to see answer by josgarithmetic(39617)

Question 1185819: Find the length of each leg of an isosceles right triangle whose hypotenuse is 12.
Click here to see answer by ikleyn(52780)

Question 1186297: Carrie works dues south of her apartment. Her friend Sarah works due east of the apartment. They leave for work at the same time. By the time Carrie is 5 miles form their apartment, the distance between them is 1 mile more than Sarah’s distance from the apartment. How far from the apartment is Sarah?
Click here to see answer by greenestamps(13200)

Question 1186306: A guy wire is attached to a telephone pole. The distance from the point where the wire touches the ground to the base of the telephone pole is 4 feet less than the length of the wire. How far up the telephone pole is the wire attached if the distance from the ground to where the wire is attached to the pole is 2 feet less than the length of the wire?
Click here to see answer by ikleyn(52780)

Question 1186318: Mark travels due north from home. His wife Kay works due west. They leave for work at the same time. By the time Mark is 10 miles from home, the distance between them is 2 miles more than Kay’s distance from home. How far from home is Kay?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1186317: Joe cuts out a piece of paper in the shape of a right triangle. The longer leg of the triangle is 20 inches longer than twice the length of the shorter leg. The hypotenuse is 30 inches longer than twice the length of the shorter leg. What is the length of the longer leg?
Click here to see answer by greenestamps(13200)

Question 1187325: The shortest leg of a triangle is 17 centimeters shorter than the other leg. The hypotenuse of this triangle is 25 centimeters. What are the lengths of the two legs of this triangle?

The shortest leg is centimeters long.

The other leg is centimeters long.

Click here to see answer by ikleyn(52780)

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