Download Law of Sines Finding a missing angle

Geometry/Trig
Name: ________________________________
Date: ________________________
Lesson 11-2: Law of Sines
Today’s Learning Goal: How can we use the Law of Sines to solve for missing angles in a non-right
triangle?
Warm-Up:
1. Solve for the missing side x to the nearest tenth in the diagram below.
2. Use the Law of Sines to solve for ∠R to the nearest degree.
How is this question similar to the first question
in the warm-up?
How is this question different than the first
question in the warm-up?
Geometry/Trig
Law of Sines Finding a missing angle
When do we use the law of sines?

We still use the law of sines when we are given ____________ angles and ______________ sides,
including the piece we are trying to find.

Law of Sines:
𝑎
𝑆𝑖𝑛(𝐴)
=
𝑏
𝑆𝑖𝑛(𝐵)
Steps for solving for a missing angle
1. The ratio is always set up with the side over the sine of the _______________________ angle
2. Plug in the given information
3. Cross multiply then divide to get Sin(A) by itself on one side of the equation
4. Plug into the calculator
5. Perform inverse sine on the “ANS” you have in your calculator
Let’s practice our algebra skills!
Solve the following equations for the given variable to the nearest degree:
23
20
16
123
1)
=
2)
=
𝑆𝑖𝑛(110)
𝑆𝑖𝑛(𝐶)
𝑆𝑖𝑛(𝐵)
𝑆𝑖𝑛(115)
Let’s answer the second question from the warm-up!
1. Use the Law of Sines to solve for ∠R to the nearest degree. (follow the steps above!)
Calculator steps:
1.
2. Then press sin-1
So that it looks like:
Geometry/Trig
Let’s try one more!
2. In the triangle DEF, angle D is 72o, side EF is 12.1cm, and side ED is 4.5 cm. Find angle F to the
nearest hundredth of a degree.
You try some!
3. In triangle RST, m<R = 105º, r = 12, and t = 10. Find the m<T, to the nearest degree.
4. In triangle QRS, m∠Q = 33°, RS = 12, and QS = 15. Find m∠R to the nearest hundredth. [HINT:
Draw a picture!]
Geometry/Trig
5. In triangle FUN, UN = 4, FU = 8, and
. Find m∠N to the nearest degree.
6. Solve for side AB using the Law of Sines. Round your answer to the nearest tenth.
7. a. Find side AC, to the nearest whole number.
b. Find side CB to the nearest whole number.