Lesson 8

Sine and Cosine in the Same Right Triangle

View Student Lesson

Problem 1

Select all the true equations. 

A:

\(\cos(15)=\sin(15)\)

B:

\(\cos(75)=\sin(15)\)

C:

\(\cos(75)=\cos(15)\)

D:

\(\cos(15)=\sin(75)\)

E:

\(\tan(15)=\tan(75)\)

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 2

Write 2 expressions that can be used to find the value of \(x\).

Right triangle A B C with right angle C. Angle A is 25 degrees and angle B is 65 degrees. Side A B is 11, B C is y and A C is x.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 3

Andre and Mai are discussing how to solve for side \(AB\). Andre thinks he can use the equation \(\tan(12)=\frac{x}{6}\) to solve for \(AB\). Mai thinks she can use the equation \(\tan(78)=\frac{6}{x}\) to solve for \(AB\). Do you agree with either of them? Show or explain your reasoning. 

Triangle A, B C. Angle A is right. Angle C is 12 degrees. Side A, C length 6, side A, B length x.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 4

Technology required. Jada is visiting New York City to see the Empire State building. She is 100 feet away when she spots it. To see the top, she has to look up at an angle of 86.1 degrees. How tall is the Empire State building?

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 7.)

Problem 5

Technology required. Find the missing measurements in triangle \(ABC\).

Right triangle abc. Side BC = 9 units, angle C = 35 degrees. Angle a = 90 degrees 

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 7.)

Problem 6

Right triangle \(ABC\) is shown. 

Write 2 expressions which are equal to the length of side \(BC\).

Triangle A B C. Angle C is a right angle, angle B is 55 degrees, A C is 4 point 9 units, and A B is 6 units.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 6.)

Problem 7

A triangle has sides with lengths 7, 24, and 25.

  1. Verify this is a Pythagorean triple.
  2. Approximate the acute angles in this triangle.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 5.)

Problem 8

Priya is playing hand ball and wants the ball to bounce off wall \(CB\) and land at \(D\). The court is 20 feet wide and 34 feet deep. Where on the wall should she aim if she's standing at point \(A\)?

Rectangular handball court.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 3, Lesson 16.)