Question

2. Use the following picture for this question:

a. Find both the exact and approximate value of the blue dotted side (rounded to the nearest tenth).
b. Use your approximate answer from part a to find the side length of x. Round your answer for x to the nearest tenth.

Answer 1

a.
`24√(3)` and 41.6

b. 52.1

Explanation:

a.

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

Note: the exact value of tan 60 is
`√(3)`

Thus, we can write
`Tan(60)=(y)/(24)\\y=24*Tan(60)\\y=24*√(3) \\y=24√(3)`

Approximate value (rounded to nearest tenth):
`24√(3) =41.6`

b.

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

`Sin(53)=(41.6)/(x)\\x=(41.6)/(Sin(53))=52.1`