Question

A right-angled triangle and two equations are shown below.

All lengths are given in metres.
a) Which equation is correct: equation A or equation B?
b) Use the correct equation from part a) to calculate the
length x.
Give your answer in metres to 1 d.p.
4.7
67°
x
A sin 67° =
B sin 67°:
4.7
x
a
4.7

Answer 1

a) An equation that is correct is: equation B.

b) By using the correct equation from part a, the length of x is 4.3 units.

In order to determine the length of x, we would apply the basic sine trigonometric ratio because the given side lengths represent the opposite side (x) and hypotenuse (4.7) of a right-angled triangle;

sin(θ) = Opp/Hyp

Where:

• Opp represent the opposite side of a right-angled triangle.
• Hyp represent the hypotenuse of a right-angled triangle.
• θ represent the angle.

Part a.

Based on the right-angled triangle, an equation for the sine trigonometric ratio is given by;

sin(θ) = Opp/Hyp

sin(67°) = x/4.7

Part b.

Now, we can determine the value of x as follows;

x = 4.7sin(67°)

x = 4.3264 ≈ 4.3 units.