John is painting a picture.He has green, red, yellow, purple, orange and blue paint. He wants to use four different colors on th
2 answers:
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The laws of cosine and sine and the given parameters can be used to
calculate the measure of angles and distances.
Correct responses:
Question 1: A. m∠C = 76°, a = 7.84, b = 4.37
Question 2: C. 1 triangle
Question 3: D. 31.2 miles
Question 4: A. b = 10.799
Question 5: C. 28.9°
<h3>Methods and calculations used to obtain the above responses </h3>Question 1:
If m∠A = 72°
m∠B = 32°
c = 8
Therefore;
m∠C = 180° - 72° - 32° = 76°
The correct option is therefore;
- <u>A. m∠C = 76°, a ≈ 7.84, b ≈ 4.37</u>
Question 2
The given parameters are;
a = 20
b = 10
Therefore, by the law of cosine we have;
- b² = a² + c² - 2·a·c·cos(B)
Which gives;
10² = 20² + c² - 2×20×c×cos(30°)
100 = 400 + c² - 20·c·(√3)
c² - 20·√3 ·c + 300 = 0
Therefore, given that <em>c</em> has only one value, the three sides of the triangle are known, and the number of triangles unique triangles by Side-Side-Side description is; <u>C. 1 triangle</u>
Question 3
The distance between the weather station = 24 miles
The bearing of the storm from weather station A = N17°W
The bearing of the storm from weather station B = N48°W
The angle formed at point <em>C</em> in ΔABC is therefore;
108° - 42° - 107° = 31°
By sine rule, we have;
Where:
x = The distance from weather station <em>A</em> from the storm
Which gives;
- The distance from weather station <em>A</em> from the storm is <u>D. 31.2 miles</u>
Question 4
∠A = 52°
∠C = 57°
Side BC = 9
Therefore;
∠B = 180° - 52° - 57° = 71°
∠B = 71°
According to the law of sines, we have;
Therefore;
- The correct option is; <u>A. b = 10.799</u>
Question 5
Given:
Label of the vertex of the triangle formed are; The golfer, spectator, hole
Distance from the golfer to the hole = 200 yards
Distance from the golfer to the spectator = 140 yards
Vertex angle at the spectator = 110°
By using the law of sines, we have;
Therefore;
The angle at the hole, ∅ = arcsin(0.7×sin(110°)) ≈ 41.13°
Therefore;
The angle that the golfer has = 180° - 110° - 41.1° = 28.9°
- The angle that the golfer has between the spectator and the hole is <u>C. 28.9°</u>
Learn more about law of cosine and sine here: