Question

Find the value of the letter in each of the following. Give your answers to 1 d.p.

Answer 1

Answer:

a) z = 70.5°

b) s = 83.6°

c) x = 0.7cm

Step-by-step explanation:

We would solve for the above questions using Trigonometric functions of either Sine, Cosine or Tangent.

a) We are given the following values

Hypotenuse = 21 inches

The triangle is divided into two to give us a right angle triangle

The adjacent side = 14inches/2 = 7 inches

We are to find Angle z

The Trigonometric function we are using is Cosine

cos z = Adjacent / Hypotenuse

cos z = 7/21

cos z = 1/3

z = arc cos(1/3)

z = 70.528779366°

To 1 decimal place

z = 70.5°

b) We are given the following values

Hypotenuse = 12 cm

The triangle is divided into two to give us a right angle triangle

The opposite side = 16cm/2 = 8 cm

We are to find Angle s, but it is split into 2

So we represent the half as x

The Trigonometric function we are using is Sine

sin x = Opposite/ Hypotenuse

sin x = 8/12

sin x = 2/3

x = arc sin(2/3)

x = 41.810314896°

Remember in the question, we are to find s.

s = x° × 2

s = 41.810314896 × 2

s = 83.620629792

To 1 decimal place

s = 83.6°

c) From the above diagram, we are to find the Opposite side represented by x

Our triangle is split into two equal halves

Adjacent side = 2cm

Angle θ = 36°/2 = 18°

We are using Trigonometric function tan to solve for question c

tan θ = Opposite/ Adjacent

tan 18° = Opposite/ 2

Cross Multiply = tan 18° × 2

0.3249196962 × 2

= 0.726542528cm

To one decimal place,

x = 0.7cm