SOLUTION: Find the area in {{{ cm^2 }}}, of a right triangle that has one acute angle to twice the other, and has a hypotenuse equal to 5 cm.
A) 6
B) {{{ 25sqrt(3)/8 }}}
C) {{{ 25sqrt(3)/
Algebra.Com
Question 911743: Find the area in , of a right triangle that has one acute angle to twice the other, and has a hypotenuse equal to 5 cm.
A) 6
B)
C)
D) 12
E)
Found 2 solutions by ichigo449, josmiceli:
Answer by ichigo449(30) (Show Source): You can put this solution on YOUR website!
Let x be one of the acute angles. Then, as we have a right triangle, we obtain the equation: 3x+90=180, or x = 30 so 2x = 60, and we have a 30-60-90 triangle. Now, we have many ways to proceed to find an answer and I suggest you try to find 3 separate ways to get the area from this step. I will give you one as follows: Let H be the hypotenuse of the triangle, then for a 30-60-90 triangle the shortest side is H/2, and the middle length side is 1/2(H*sqrt(3)). Knowing these facts we can express the area as: H^2*sqrt(3)/8 by the regular area = 1/2(base*height) with base = H/2 and height = 1/2(H*sqrt(3)). We therefore conclude, by plugging in H = 5 that the answer is B. Have a nice day and good luck with your class.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let the smallest angle =
The next larger angle =
It's a right triangle so the 3rd angle is
It is a 30-60-90 triangle
The sides are in the ratios:
, , and
------------------------------
The actual lengths of the sides are:
, , and
----------------------------------
-----------------------
The answer is ( B )
RELATED QUESTIONS
Suppose a right triangle has a hypotenuse which is 2 cm longer than one leg and 9 cm... (answered by stanbon)
Find the missing side and the hypotenuse of a right triangle that has one side equal to... (answered by josgarithmetic)
In a right triangle, the length of one of the legs is 8 cm and the measure of the acute... (answered by josmiceli,ikleyn,Theo,MathTherapy)
please help me solve this word problem:
A right triangle has has one leg that is 5 cm... (answered by irshad_ahmed0@yahoo.com)
The hypotenuse of a right triangle is 2 cm longer than one leg, The other leg has length... (answered by ikleyn)
A right triangle has a fixed hypotenuse of 30 cm. And the other two sides are allowed to (answered by KMST)
If a right triangle has an area of 54 cm squared and one of the legs is 9 cm long, how... (answered by TimothyLamb)
if a right triangle has a hypotenuse of 12 cm and one leg that measures 9 cm, what is the (answered by TimothyLamb)
if a right triangle has a area 180cm^(2) and hypotenuse 41 cm, find the length of the two (answered by drj)