Question

In a right triangle ø is an acute angle and secø= 10/3 what is the exact value of sin ø

Answer 1

Recall,

Secø = 1/Cosø

Given that

secø= 10/3, it means that

1/Cosø = 10/3

If we reverse both sides of the equation, it means that

Cosø/1 = 3/10

Cosø = 3/10

Recall, Cosø = adjacent side/hypotenuse

Thus,

adjacent side = 3

hypotenuse = 10

We would draw the right angle triangle below

looking at the right angle triangle,

opposite side = x

To find x, we would apply the pythagorean theorem which is expressed as

hypotenuse^2 = opposite side^2 + adjacent side^2

`\begin{gathered} 10^2=x^2+3^2 \\ 100=x^2\text{ + 9} \\ x^2\text{ = 100 - 9 = }91 \\ x\text{ = }\sqrt[]{91}\text{ = 9.54} \end{gathered}`

We know that

Sinø = opposite side/hypotenuse

Sinø = 9.54/10

Sinø = 0.954