Question

How do I calculate the height of the semi-truck using sine?

While on icy roads, a semi truck slid into a ditch and the back part of the semi truck began to tip, hitting a light post and breaking it 2.7 m up the base. The top portion of the light post was now touching the ground. The angle which the top of the light post made with the ground is 62 degrees. How tall to the nearest tenth of a meter was the light post before it was broken? I started the problem by taking the SINE of 62 degrees and making a proportion.

.88 X
_ X _
1 2.7
.88 * 2.7 = 2.376
ANS: 2.7 + 2.376 = 5.076. Am I correct?

Answer 1

`5.8` m

Explanation:

Let `AB and BC` be the bottom portion and the top portion of the light post, respectively, as shown in the figure.
Let `BC=x`
In `DeltaABC', xsin62=2.7`,

`=> x=2.7/sin62~~3.058` m `=3.1` m (to the nearest tenth of a meter)

Hence , height of light post before it was broken :
`h=AB+BC=AB+x=2.7+3.1=5.8` m