contestada

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

Respuesta :

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:

C. [tex]sin(\angle H)=cos(\angle H)[/tex]

Step-by-step explanation:

Givens

[tex]\triangle HJK[/tex] is a right triangle.

[tex]m \angle J = 90\°[/tex]

[tex]tan (\angle H) = 1[/tex]

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

[tex]tan(\angle H) = \frac{JK}{JH}=1[/tex]

Also, we can deduct that the angle [tex]\angle H[/tex] 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 [tex]\angle H[/tex], we can find the rest of trigonometric reasons

[tex]sin(\angle H)=sin (45\°)=\frac{\sqrt{2} }{2} \\\\cos(\angle H)=cos(45\°)=\frac{\sqrt{2} }{2}[/tex]

Basically, this means that both reasons are equal

[tex]sin(\angle H)=cos(\angle H)[/tex]

Therefore, the right answer is C.

Otras preguntas