Malaya is standing directly between a 90-foot tall courthouse and a 54-foot tall bank. If the angle of elevation from the point where Malaya is standing to the top of the courthouse is 72°, while the angle of elevation to the top of the bank is 35°. What is the distance between the courthouse and the bank?

Step-by-step explanation:

Draw a picture.

c and b are Malaya’s distance from the courthouse and bank, respectively.

tan(72°) = c/90

c = 90tan(72°)

tan(35°) = b/54

b = 54tan(35°)

Distance between courthouse and bank = c+b

= 90tan(72°) + 54tan(35°)

= 301.5 ft

look a the sides they are perpendicular

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.