Answer:
a) z = 70.5°
b) s = 83.6°
c) x = 0.7cm
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