Lesson Example Discussion Quiz: Class Homework |
Quiz At Home |
Title: Law of sines and cosines |
Grade: 1400-a Lesson: S3-L7 |
Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts. |
Quiz: at Home
| Problem Id | Problem | Options |
|---|---|---|
1 |
Given a triangle ABC with side lengths a = 20, b = 25, and angle C = 120 degrees, find the remaining side lengths and angles of the triangle. |
A) Side c = 30, Angle A = 30 degrees, Angle B = 30 degrees B) Side c = 15, Angle A = 30 degrees, Angle B = 30 degrees C) Side c = 25, Angle A = 40 degrees, Angle B = 20 degrees D) Side c = 30, Angle A = 40 degrees, Angle B = 20 degrees |
2 |
Given a quadrilateral ABCD with side lengths AB = 8, BC = 15, CD = 12, and angle B = 120 degrees, find the maximum possible area of the quadrilateral. |
A) 60 square units B) 72 square units C) 80 square units D) 90 square units |
3 |
A ship leaves port A and sails 120 miles due east to port B. Then, it changes course and sails 200 miles on a bearing of 120 degrees. Find the distance and bearing from port B to the point where the ship is now. |
A) Distance = 180 miles, Bearing = 60 degrees B) Distance = 180 miles, Bearing = 240 degrees C) Distance = 220 miles, Bearing = 60 degrees D) Distance = 220 miles, Bearing = 240 degrees |
4 |
Consider triangle XYZ with side lengths x = 6, y = 8, and z = 10. What is the measure of angle Z, rounded to the nearest degree? |
A) 36 degrees B) 48 degrees C) 60 degrees D) 53 degrees |
5 |
An observer on a cliff measures the angles of depression to two ships in the ocean. The angles of depression are 30 degrees and 45 degrees, and the distance between the ships is 10 kilometers. Determine the distance from each ship to the observer using the Law of Sines and Cosines. |
A) 5 km and \$5\sqrt3\$ km B) 5 km and 5 km C) \$5sqrt3\$ km and 10 km D) 5 km and \$10sqrt3\$ km |
6 |
A kite has a diagonal of length 30 meters and one angle measuring 60 degrees. The two non-right angles of the kite are congruent. Find the length of the shorter diagonal of the kite. |
A) 25 meters B) 40 meters C) 30 meters D) 35 meters |
7 |
Two chords intersect inside a circle with a radius of 10 cm. The chords have lengths of 16 cm and 12 cm and the smaller chord is bisected by the larger chord at the intersection point. Find the distance between the centers of the two chords. |
A) 11.1 cm B) 12.8 cm C) 13.4 cm D) 14.5 cm |
8 |
A person stands on the edge of a cliff and measures the angle of elevation to the top of a nearby building as 50°. They then walk 100 meters closer to the building and measure the angle of elevation as 60°. How tall is the building? |
A) 119.18 meters B) 129.28 meters C) 239.18 meters D) 257.28 meters |
9 |
A lighthouse is located at point A on a straight coastline. From point B, which is 500 meters down the coastline from point A, the angle of elevation to the top of the lighthouse is 30°. From point C, which is 300 meters down the coastline from point A, the angle of elevation to the top of the lighthouse is 45°. How tall is the lighthouse? |
A) 234.9 meters B) 288.7 meters C) 324.5 meters D) 312.8 meters |
10 |
An airplane is flying at an altitude of 10,000 meters. From a point on the ground directly below the airplane, the angle of elevation to the airplane is 30°. From another point 5,000 meters away from the first point, the angle of elevation to the airplane is 45°. How high is the airplane? |
A) 15,000 meters B) 12,000 meters C) 10,000 meters D) 14,000 meters |
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