Question

- In the following diagram of triangle QRS, QR = 8 and QS = 17. Determine the value of sin Q. Show how you

Answer 1

Answer:

$SinQ=\frac{15}{17}$

Step-by-step explanation:

We draw the right triangle as shown in the image attached.

Δ QRS

Where R is the right angle

Given

QR = 8

QS = 17

Now, using Pythagorean Theorem, we can find RS:

$QR^2+RS^2=QS^2\\8^2+RS^2=17^2\\RS^2=17^2-8^2\\RS^2=225\\RS=\sqrt{225}\\RS=15$

Now, we know the ratio Sine as:

$Sin(\theta)=\frac{Opposite}{Hyotenuse}$

Where $\theta$ is the angle (here angle Q)

Opposite side is RS (which is 15)

Hypotenuse is given as QS (which is 17)

So,

$SinQ=\frac{15}{17}$

This is the value of SinQ.

We don't want the angle, so we'll stop here.