Solving right triangle with hypotenuse and angle

[tcunninghamt7]

A right triangle has a hypotenuse of 10 ft. and one angle of 30°. How long is the side opposite the angle?


11.55 ft.

8.67 ft.

20 ft.

5 ft.

Mark For Later Review
Which of the other two angles is it referring too? Clearly a 30-60-90 triangle. A diagram would make this question more clear.

[Kalbi_Rob]

A right triangle has a hypotenuse of 10 ft. and one angle of 30°. How long is the side opposite the angle?


11.55 ft.

8.67 ft.

20 ft.

5 ft.

Mark For Later Review
Which of the other two angles is it referring too? Clearly a 30-60-90 triangle. A diagram would make this question more clear.

422

The angles don't matter since they give you the hypotenuse and one of the angles on the right triangle. To find the length of the opposite leg of the 30 degree angle, you only need sine and the hypotenuse.

sin⁡(θ)=opposite/hypotenuse=≫opposite=hypotenuse*sin⁡(θ)=10*sin⁡(30 )=5 FT

[martigan]

A right triangle has a hypotenuse of 10 ft. and one angle of 30°. How long is the side opposite the angle?


11.55 ft.

8.67 ft.

20 ft.

5 ft.

Mark For Later Review
Which of the other two angles is it referring too? Clearly a 30-60-90 triangle. A diagram would make this question more clear.

In a 30/60/90 triangle, the sides are x for the shortest leg, 2x for the hypotenuse, and x*SQRT(3) for the longest leg ... if 10 is the hypotenuse, then the shortest leg is half that, or 5. That means the longest leg is 5*SQRT(3), or 8.67. So, if they are asking what the side opposite the 30 degrees is, then 5 is the answer. If the side opposite the 60 degrees is, then 8.67.

You don't need sohcahtoa for a 30/60/90 triangle if they give you a value of a side. Also, remember the 1/1/SQRT(2) triangles...