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

Answer:

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

Step-by-step 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

$tan(\angle H) = \frac{JK}{JH}=1$

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

$sin(\angle H)=sin (45\°)=\frac{\sqrt{2} }{2} \\\\cos(\angle H)=cos(45\°)=\frac{\sqrt{2} }{2}$

Basically, this means that both reasons are equal

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

Therefore, the right answer is C.

Answer 2

I hope this helps you


tgH=HJ/HK


angle H+angle K=90


H=K=45 degree


sin45=cos46 = square root of 2/2