Question

Find the value of x. Round the length to the nearest tenth.

500 m
A. 777.9 m
40°
Not drawn to scale
B. 595.9 m
C. 321.4 m
D. 652.7 m

Answer 1

Explanation:

The 40 degree angle we are given is called an angle of depression. Because of geometry and the fact that the base of the triangle and this dotted line are parallel to one another, the base angle inside the triangle is also 40. These are called alternate interior angles. The x represents the hypotenuse of the triangle. We can use right triangle trig to find it. The side measuring 500 is OPPOSITE the reference angle of 40 and the missing side is the HYPOTENUSE, so the trig ratio we will use is sin which is, according to SohCahToa, opposite side over hypotenuse; namely:

`sin40=(500)/(x)`

Algebraically, we will multiply both sides by x and then divide by sin40 to get:

`x=(500)/(sin40)`

Make sure your calculator is in degree mode and not radian mode and enter the problem as you see it above to get that

x = 777.9m, choice A.