Q: What is the value of $$\sin(\theta) in $$terms of $$x$$ and $$u$$ for the triangle shown?

$$\sin(\theta) = \dfrac{1}{u}$$

Q: Which trigonometric ratio represents $$\tan(\theta)$$ for the triangle in the image?

$$\tan(\theta) = \dfrac{1}{x}$$

Q: If $$x = 4$$ and $$u = 5$$, what is the value of $$\cos(\theta)$$?

$$\cos(\theta) = \dfrac{4}{5}$$

Question 1

Given the right triangle in the image, if the side opposite angle $$	heta is$$ $$1$$, the side adjacent is $$x$$, and the hypotenuse is $$u$$, which equation correctly relates $$u to$$ $$x$$ using the Pythagorean Theorem?

Accepted Answer

$$u^2$$ = $$x^2 + 1$

Question 2

What is the value of $$\sin(	heta) in $$terms of $$x$$ and $$u$$ for the triangle shown?

Accepted Answer

$$\sin(	heta) = \dfrac{1}{u}$$

Question 3

If $$x = 2$$, what is the exact value of $$u$$?

Accepted Answer

$$u = \sqrt{5}$$

Question 4

Which trigonometric ratio represents $$	an(	heta)$$ for the triangle in the image?

Accepted Answer

$$	an(	heta) = \dfrac{1}{x}$$

Question 5

If $$	heta is an $$acute angle in the triangle, which of the following is always true?

Accepted Answer

$$u \u003e x \u003e 1$$

Question 6

Suppose $$\sin(	heta) = 0.6$$ for the triangle shown. What is the value of $$u$$?

Accepted Answer

$$u = \dfrac{1}{0.6}$$

Question 7

If $$x = 4$$ and $$u = 5$$, what is the value of $$\cos(	heta)$$?

Accepted Answer

$$\cos(	heta) = \dfrac{4}{5}$$

Question 8

Which of the following expressions gives $$x in $$terms of $$u$$?

Accepted Answer

$$x = \sqrt{u^2$ - 1}$$

Question 9

If $$	an(	heta) = 0.5$$ and the side opposite $$	heta is$$ $$1$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 10

A ladder leans against a wall forming a right triangle as shown, with the ground as $$x$$, the wall as $$1$$, and the ladder as $$u. If $$the ladder is $$13$$ feet long and the wall is $$5$$ feet high, how far is the base of the ladder from the wall?

Accepted Answer

$$x = \sqrt{13^2$ - 5^2$}$$

Guided Practice: Establishing Trigonometric Identities Using Right Triangles

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