Question

In AOPQ, the measure of ZQ=90°, Q0 = 6.4 feet, and PQ = 3.8 feet. Find themeasure of ZP to the nearest tenth of a degree.

Answer 1

Angle P = 59.3°

Step-by-step explanation

To answer this, we will first sketch the triangle OPQ

Let the unknown Angle P be x

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is x, the trignometric ratios in short forms are written as

SOH, CAH and TOA

SOH means Sin x = (Opp/Hyp)

CAH means Cos x = (Adj/Hyp)

TOA means Tan x = (Opp/Adj)

So, the one to be used depends on the sides of the triangle that are provided.

For this triangle,

Hypotenuse = OP = ?

Opposite = OQ = 6.4

Adjacent = PQ = 3.8

Angle = x = ?

TOA means Tan x = (Opp/Adj)

Tan x = (6.4/3.8)

Tan x = 1.6842

x = Tan⁻¹ (1.6842)

x = 59.3°

Hope this Helps!!!