Question

Instructions: Find the missing side. Round your answer to the nearesttenth.59028XX=

Answer 1

Given the ΔABC below:

To find the missing side,

Step 1: Identify the sides of the triangle.

Thus,

`\begin{gathered} hypotenuse\Rightarrow AB(longest\text{ side of the triangle\rparen} \\ opposite\Rightarrow AC(side\text{ facing the angle\rparen} \\ adjacent\Rightarrow BC \end{gathered}`

Step 2: Evaluate the value of x, using trigonometric ratios.

From trigonometric ratios,

`\cos\theta=(adjacent)/(hypotenuse)`

where

`\theta=\angle B`

Thus,

`\begin{gathered} \cos B=(adjacent)/(hypotenuse) \\ =(BC)/(AB) \\ \Rightarrow\cos B=(x)/(28) \\ cross-multiply, \\ x=28*\cos B \\ but\text{ B=59} \\ \Rightarrow x=28*\cos59 \\ =28*0.5150380749 \\ =14.4210661 \\ \Rightarrow x\approx14.4 \end{gathered}`

Hence, the value of x, to the nearest tenth, is

`14.4`