b What is the measure of the unknown non-right angle in the triangle? What does the sine ratio measure?
A
a cos 58.5^(∘) = x/7
B
b x≈ 3.6
Practice makes perfect
a The triangle we have been given is a right triangle where the hypotenuse and a non-right angle is known. Since we want to determine the known angle's adjacent leg, we can use the cosine ratio.
b If we subtract the known angles from 180^(∘) we can determine the unknown angle.
180^(∘)-90^(∘)-58.5^(∘)=31.5^(∘)
The sine ratio is the opposite side divided by the hypotenuse.
Since sin 31.5^(∘)≈ 0.522 and both sin 31.5^(∘) and cos 58.5^(∘) equals x7, we can write and solve an equation containing x.
x/7≈ 0.522 ⇔ x≈ 3.6
