Question

Find the value of x in the triangle shown below

Answer 1

55.52

Explanation:

By sine rule:

`( \sin x \degree)/(5) = ( \sin 70 \degree)/(5.7) \\ \\ \sin x \degree = ( 5 \: \sin 70 \degree)/(5.7) \\ \\ \sin x \degree = ( 5 \: \sin 70 \degree)/(5.7) \\ \\ x \degree = {sin}^( - 1) ( ( 5 \: \sin 70 \degree)/(5.7)) \\ \\ x \degree = 55.516753493 \degree\\ \\ x = 55.52`

Answer 2

x = 55

Explanation:

Since 2 sides of the triangle are congruent, both 5, then the triangle is isosceles and the 2 base angles are congruent, both x , then

x + x + 70 = 180 ← sum of 3 angles = 180°

2x + 70 = 180 ( subtract 70 from both sides )

2x = 110 ( divide both sides by 2 )

x = 55