Question

In ΔNOP, the measure of ∠P=90°, the measure of ∠N=59°, and PN = 7.4 feet. Find the length of OP to the nearest tenth of a foot.

Answer 1

12.3 feet

Explanation:

tan 59= 7.4 / x

​ 7.4 tan 59 =x

x = 12.3157 ≈ 12.3 feet

Answer 2

OP is 12.3 feet

Explanation:

Please refer to the attachment for the diagrammatic representation.

In the right angled triangle, we are told to obtain the length OP

To do this, we have to see what we have.

From the diagram, with respect to the given angle, the length OP is the opposite, while the length NP is the adjacent. So what is needed now is the trigonometric identity that links the opposite and the adjacent together.

The trigonometric identity that does this is the tan

By definition; tan of an angle = length of the opposite/ length of the adjacent

Hence;

Tan 59 = OP/7.4

OP = 7.4 Tan 59

OP = 7.4 * 1.6643

OP = 12.3 feet