Answer:
d. 21.5
Step-by-step explanation:
To find the missing side length of each triangle, use the pythagorean theorem. The theorem is where a, b, and c are all side lengths of the triangle. a is the smallest lef and b is the other leg while c is always the hypotenuse or longest side.
In d, you'll use it twice to find the missing measure. First use it when a = 12 and b = 20. So you'll have:
Repeat the same process using a = 9 and c = 23.32. Then solve for the b value.
=============================================
Explanation:
Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.
Focus on triangle BCD.
The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.
We know that he's 14 ft off the ground, which explains why AB = CD = 14.
The goal is to find BC = AD = x.
---------------------------
Again, keep your focus on triangle BCD.
We'll use the tangent ratio to say
tan(angle) = opposite/adjacent
tan(B) = CD/BC
tan(30.26) = 14/x
x*tan(30.26) = 14
x = 14/tan(30.26)
x = 23.9965714046732
That value is approximate. Make sure your calculator is in degree mode.
That value rounds to 24 feet when rounding to the nearest whole foot.
