Question

A person standing 130 feet from the base of a building. the angle of elevation from the sidewalk to the too of the building is 68°. find the height of the building.

Answer 1

A person standing 130 feet from the base of a building. the angle of elevation from the sidewalk to the top of the building is 68°. find the height of the building. ​

We need to sketch the diagram to show a clearer picture of the question.

This is an application of Trigonometrical identities.

In this case, we are considering the tangent of an angle, because we have values of the opposite and adjacent in the triangle.

`\begin{gathered} \tan 68^0\text{ = }(h)/(130)\text{ ( because tan }\theta\text{ = }\frac{opposite}{\text{adjacent}}\text{ )} \\ \\ We\text{ n}eed\text{ to cross-multiply and then we have :} \\ h=130Xtan68^0 \\ h\text{ = 130 x 2.4751} \\ h=\text{ }321\text{ . 763 m} \\ h\text{ = 321. 8 m ( correct to 1 decimal place )} \end{gathered}`

CONCLUSION :

The height of the building is h = 321. 8 m ( correct to 1 decimal place).