Question

In right triangle HJK, angle J is a right angle and tan angle H = 1. Which Statement about triangle HJK MUST BE TRUE? A. Sin angle H =1/2. B. Sin angle H = 1. C. Sin angle H = Cos angle H. D. Sin angle H = 1 divided by Cos angle h

Answer 1

I hope this helps you


tgH=HJ/HK


angle H+angle K=90


H=K=45 degree


sin45=cos46 = square root of 2/2

Answer 2

C.
`sin(\angle H)=cos(\angle H)`

Explanation:

Givens

`\triangle HJK` is a right triangle.

`m \angle J = 90\°`

`tan (\angle H) = 1`

We this information, we can deduct that the opposite leg to
`\angle H` is JK, and the adjacent leg to
`\angle H` is JH. So, if
`tan (\angle H) = 1`, this means that both legs are equal, because to result the tangent in 1, both legs have to be equal

`tan(\angle H) = (JK)/(JH)=1`

Also, we can deduct that the angle
`\angle H` is equal to 45°, because when the tangent is equal to one unit, that means the triangle is symmetric, which means that its angles are 45°.

So, with knowing the measure of
`\angle H`, we can find the rest of trigonometric reasons

`sin(\angle H)=sin (45\°)=(√(2) )/(2) \\\\cos(\angle H)=cos(45\°)=(√(2) )/(2)`

Basically, this means that both reasons are equal

`sin(\angle H)=cos(\angle H)`

Therefore, the right answer is C.