Question

Find the size of angle BAC Give your answer to 3 significant figures

Answer 1

Answer:

angle BAC = 50.5°

Step-by-step explanation:

To find the size of angle BAC, we will follow the steps below;

First, we will use Pythagoras theorem to find side AC

from the diagram, AB = 14 cm       BC = 17 cm

Using Pythagoras theorem,

AC² = AB² + BC²

        = 14² + 17²

         =196 +289

           =485

AC² = 485

Take the square root of both-side

AC = √485

AC = 22 .023

AC = 22.023 cm

angle <B = 90°

Using the sine rule,

$\frac{sin A}{a}$   =  $\frac{sin B}{b}$

A = ?

a=BC = 17 cm

B = 90°

b = AC = 22.023 cm

we can now [proceed to insert the values into the formula and then solve for A

$\frac{sin A}{a}$   =  $\frac{sin B}{b}$

$\frac{sin A}{17}$  = $\frac{sin 90}{22.023}$

cross - multiply

22.023× sinA = 17× sin90

Divide both-side of the equation by 22.023

sin A = 17 sin90 / 22.023

sin A = 0.771920

Take the sin⁻¹ of both-side of the equation

sin⁻¹sin A = sin⁻¹0.771920

A = sin⁻¹0.771920

A≈ 50.5°

Therefore, angle BAC = 50.5°