1. what is the value of x in the triangle?
enter your answer in the box. round your final answer to the nearest hundredth.
x = cm

2. what are the values of the trigonometric ratios for this triangle?
drag the answer into the box to match each ratio.
sinθ
cosθ
tanθ
options you can drag
5/4
3/4
3/5
4/3
4/5
5/3

3. what is the value of x in this triangle?
enter your answer as a decimal in the box. round only your final answer to the nearest hundredth.
x = °

4. what is the value of θ for the acute angle in a right triangle?
sin(θ)=cos(58°)
enter your answer in the box.
θ= °

5. a party tent is used for an outdoor event. ropes of equal length support each tent pole. the angle the rope makes with the floor is 55°.
what is the height of each pole?
enter your answer in the box. round only your final answer to the nearest tenth.

6. what is the exact value of sin 60° ?
enter your answer, as a simplified fraction, in the box.

Problem 1

cos(angle) = adjacent/hypotenuse
cos(18) = x/25
25*cos(18) = x
x = 25*cos(18)
x = 23.7764129073789
x = 23.78

x = 23.78

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Problem 2

theta = greek letter that looks like a "zero" or the letter O with a horizontal line through it

With the reference angle of theta, the opposite side is 3. This side is the leg furthest from the angle theta. In contrast, the side 4 is the closest leg to theta. The longest side 5 is the hypotenuse. The hypotenuse is always the lonest side

sin(theta) = opposite/hypotenuse
sin(theta) = 3/5

cos(theta) = adjacent/hypotenuse
cos(theta) = 4/5

tan(theta) = opposite/adjacent
tan(theta) = 3/4

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In summary:
sin(theta) = 3/5
cos(theta) = 4/5
tan(theta) = 3/4

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Problem 3

cos(angle) = adjacent/hypotenuse
cos(x) = 15/29
x = arccos(15/29) .... inverse cosine or cos^(-1) also works
x = 58.852610078491
x = 58.85

x = 58.85

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Problem 4

The rule we'll use is
sin(x) = cos(90-x)

sin(theta) = cos(90-theta)
cos(90-theta) = cos(58)
90 - theta = 58
90 - theta+theta = 58+theta
90 = 58+theta
90-58 = 58+theta-58
32 = theta
theta = 32

32

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Problem 5

x = height of pole

the vertical side is the side we want, which is the opposite side compared to the angle 55 degrees

sin(angle) = opposite/hypotenuse
sin(55) = x/25
25*sin(55) = x
x = 25*sin(55)
x = 20.4788011072248
x = 20.5

Each pole is roughly 20.5 feet tall.

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Problem 6

The exact value is the fraction sqrt(3)/2 which can be written as

"sqrt" is shorhand for "square root"