Question

Solve for x round to the nearest tenth if necessary

Answer 1

2.8

Explanation:

1. c = a · sin(C) / sin(A)

This is the equation to find x. Let's see what we have.

c = x

a = 5.7

C = 26

A = ?

Let's find A. We know B is 90 and C is 26. Triangle Sum Theorem time!

2. 180 = 90 + 26 + A

180 = 116 + A

64 = A

A = 64

We found A. Let's see what we have now!

c = x

a = 5.7

C = 26

A = 64

Let's solve the equation now.

3. x = 5.7 · sin26 / sin64

Let's use a calcalator to find the answer.

4. 2.78008 = 5.7 · sin26 / sin64

5.7 · sin26 / sin64 = 2.78008

We should round this to the nearest tenth. 7 is in the tenth place. Though 8 is behind 7. 8 is greater than 4 which means 7 must be rounded up.

5. 2.8 is the answer.

Answer 2

x ≈ 2.8

Explanation:

Using the tangent ratio in the right triangle

tan26° =
`(opposite)/(adjacent)` =
`(CD)/(DE)` =
`(x)/(5.7)` ( multiply both sides by 5.7 )

5.7 × tan26° = x , then

x ≈ 2.8 ( to the nearest tenth )