The Standard Law of Sines: Trigonometry problems

User Generated

RBcryy

Mathematics

Description

Directions: Solve each of the following problems

Unformatted Attachment Preview

Review Directions: Solve each of the following problems. 1. In AABC, sin A = 77, sin C = 23 and c = 16. Find the length of A. 2. In APQR, side Q = 25, m
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

The solutions are ready!

The sine theorem:
π‘Ž
𝑏
𝑐
=
=
.
sin 𝐴 sin 𝐡 sin 𝐢
In this context, angles are denoted with capital letters (the angle vertex),
while sides β€” with small letters (side π‘Ž is opposite to the angle 𝐴).

1. 𝐴 = 77Β°, 𝐢 = 23Β°, 𝑐 = 16, find π‘Ž.
π‘Ž

𝑐

sin 𝐴

sin 77Β°

= sin 𝐢, i.e. π‘Ž = 𝑐 βˆ™ sin 𝐢 = 16 βˆ™ sin 23Β° β‰ˆ πŸ‘πŸ—. πŸ—.
sin 𝐴

2. π‘ž = 25, 𝑃 = 13Β°, 𝑄 = 70Β°, find 𝑝.
𝑝

π‘ž

sin 𝑃

sin 13Β°

= sin 𝑄, i.e. 𝑝 = π‘ž βˆ™ sin 𝑄 = 25 βˆ™ sin 70Β° β‰ˆ πŸ”. 𝟎.
sin 𝑃

3. 𝑦 = 18, π‘Œ = 39Β°, 𝑍 = 51Β°, find 𝑧.
𝑦
sin π‘Œ

𝑧

sin 𝑍

sin 51Β°

= sin 𝑍, i.e. 𝑧 = 𝑦 βˆ™ sin π‘Œ = 18 βˆ™ sin 39Β° β‰ˆ 𝟐𝟐. 𝟐.

4. 𝑏 = 27, 𝐴 = 82Β°, 𝐡 = 58Β°, find π‘Ž.
π‘Ž
sin 𝐴

𝑏

sin 𝐴

sin 82Β°

= sin 𝐡, i.e. π‘Ž = 𝑏 βˆ™ sin 𝐡 = 27 βˆ™ sin 58Β° β‰ˆ πŸ‘πŸ. πŸ“.

5. 𝑑 = 9, 𝑇 = 29Β°, 𝑃 = 110Β°, find 𝑝.
𝑝
sin 𝑃

𝑑

sin 𝑃

= sin 𝑇, i.e. 𝑝 = 𝑑 βˆ™ sin 𝑇 = 9 βˆ™

sin 110Β°
sin 29Β°

β‰ˆ πŸπŸ•. πŸ’.

6. 𝑒 = 22, 𝐸 = 81Β°, 𝐺 = 26Β°, find 𝑔.
𝑒
sin 𝐸

𝑔

sin 𝐺

sin 26Β°

= sin 𝐺 , i.e. 𝑔 = 𝑒 βˆ™ sin 𝐸 = 22 βˆ™ sin 81Β° β‰ˆ πŸ—. πŸ–.


The sine theorem:...


Anonymous
Just what I needed…Fantastic!

Studypool
4.7
Indeed
4.5
Sitejabber
4.4

Similar Content

Related Tags