SOLUTION: Use the markings in the image to answer the following questions (drawing not to scale): https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.2-HOT1-Tris.jpg

Algebra ->  Trigonometry-basics -> SOLUTION: Use the markings in the image to answer the following questions (drawing not to scale): https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.2-HOT1-Tris.jpg       Log On


   

Question 1042766: Use the markings in the image to answer the following questions (drawing not to scale):
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.2-HOT1-Tris.jpg
a. As you look at sides a, b, c, and d, which side lengths are possible to calculate based on the information in the image?
b. For those side lengths which are possible to calculate, what steps would you take to calculate each side?
c. For those side lengths we don’t have enough information to calculate, what information would you need to complete the calculations?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Three right triangles, and you know angle theta and you know main triangle's height or altitude.

GIVEN INFORMATION
system%28cos%28theta%29=5%2F13%2Cheight=12%29

The complementary angle at the top is 90-theta.

system%2812%2Fd=cos%2890-theta%29%2Cc%2Fd=5%2F13%29
These allow you to find c.
d%2Fc=13%2F5
d=13c%2F5
-
d%2F12=1%2Fcos%2890-theta%29
%2813c%2F5%29%2F12=cos%2890-theta%29
c=%285%2F13%29%2A12%2Acos%2890-theta%29, notice the complement angle
highlight%28c=%2860%2F13%29sin%28theta%29%29

There is a theorem about this situation of triangles allowing the statement:
sqrt%28c%2Ab%29=12
meaning cb=144.
Also meaning highlight%28b=144%2Fc%29.

Use the basic trig identity to setup sin^(theta)+(5/13)^2=1 and you will want the positive value for sin%28theta%29=sqrt%281-%285%2F13%29%5E2%29, and simplify and use this...

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Use the markings in the image to answer the following questions (drawing not to scale):
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.2-HOT1-Tris.jpg
a. As you look at sides a, b, c, and d, which side lengths are possible to calculate based on the information in the image?
b. For those side lengths which are possible to calculate, what steps would you take to calculate each side?
c. For those side lengths we don’t have enough information to calculate, what information would you need to complete the calculations?
Sides c (5) and d (13) are immediately known, based on the given Trig. Ratio



Since there are 3 SIMILAR triangles, the smallest triangle (triangle containing sides c and d) can be used to set up a

proportion with the largest triangle (containing sides a, b, c, and d), to determine side b. Since c, b, and d are now known,

side a can be found using the Pythagorean formula (a%5E2+%2B+b%5E2+=+c%5E2) in the largest triangle.

OR

Since there are 3 SIMILAR triangles, the smallest triangle (triangle containing sides c and d) can be used to set up a

proportion with the 2nd largest triangle (containing sides a and b), to determine side a. Since 2 legs of the 2nd largest 

triangle are now known (a and 12), side b can be found using the Pythagorean formula (a%5E2+%2B+b%5E2+=+c%5E2).