Question

Question
1
Question
2
Question
3
Right triangles always have an angle that is
degrees.
A)
What angle measure do right triangles always have in common?
(1 point)
units
A)
A right triangle has a hypotenuse of length 18 and an angle of 35°, with a side opposite this angle oflength 4. A second right triangle also has an angle of 35°, with a hypotenuse of length 9. Determine thelength of the side opposite the 35° angle on the second triangle.
(1 point)
The length of the side opposite
is
units.
A)
Right triangle
has side lengths
,
, and
. A second right triangle,
, has side lengths of 34, 30, and 16. First, find the ratio of the side opposite
to thehypotenuse of triangle
. Then, use this ratio to identify the side length opposite point
on thesecond right triangle.
(1 point)
ABC AB = 8 BC = 15 AC = 17
A′B′C′ ∠C
ABC C′
C′
Question
4
Question
5
The ratio of the side opposite
to the hypotenuse is
.
A)
Right triangle
has side lengths
,
, and
. Find the ratio of theside opposite
to the hypotenuse of triangle
. Express your ratio as a decimal.
(1 point)
ABC AB = 21 BC = 28 AC = 35
∠C ABC
∠C
Option #
is correct.
A)
The ratio of the side opposite
to the hypotenuse represents which trigonometric function?
Option #1:
Option #2:
Option #3:
(1 point)
θ
tan θ = opposite
hypotenuse
sin θ = opposite
hypotenuse
cos θ = opposite
hypotenuse

Answer 1

1) Right triangles always have a 90° angle.

2) Using similarity (opposite scales with hypotenuse): opposite = 4*(9/18) = 2.
The side opposite 35° on the second triangle is 2 units.

3) For △ABC with AB = 8, BC = 15, AC = 17 (hypotenuse AC): ratio opposite/hypotenuse for ∠C = AB/AC = 8/17.
For △A′B′C′ with hypotenuse 34, opposite side = (8/17)*34 = 16.

4) For △ABC with AB = 21, BC = 28, AC = 35 (hypotenuse AC): ratio opposite/hypotenuse = 21/35 = 0.6.

5) The ratio opposite/hypotenuse is sin θ (Option #2).