SaiBook.us SAT-2

Quiz At Home

Title: Trigonometry

Grade: 1300-a Lesson: T1-P1

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	Find the exact value of sin(2θ) if \$ sin(θ) = 3/5 \$ and θ is in the first quadrant.	A) \$ 24/25 \$ B) \$ 23/27 \$ C) \$ 24/29 \$ D) \$ 21/28 \$
2	The two sides of the triangle x and y are 4 times shorter than the hypotenuse. Find the value of cos a?	A) \$ 3/4 \$ B) \$ 1/4 \$ C) \$ 2/3 \$ D) \$ 6/5 \$
3	A ladder is leaning against a wall. If the foot of the ladder is 5 meters away from the wall and the ladder is 10 meters long, find the angle the ladder makes with the ground.	A) 30° B) 90° C) 60° D) 45°
4	Determine the value of cosec 150° using cofunction identities.	A) 1 B) 0 C) Undefined D) 2
5	In a bridge construction project, an engineer needs to calculate the length of a diagonal brace connecting two beams. If one beam is 15 meters long and the angle between the brace and the horizontal beam is 30∘, find the length of the diagonal brace.	A) \$ 6\sqrt3 \$ meters B) \$ 8\sqrt3 \$ meters C) \$ 4\sqrt3 \$ meters D) \$ 10\sqrt3 \$ meters
6	A person standing at point A observes the top of a tree at point T at an angle of elevation of 60 degrees. If the person walks 25 meters towards the tree to point B and observes the top of the tree at an angle of elevation of 75 degrees, calculate the height of the tree.	A) 34.25 meters B) 38.25 meters C) 43.3 meters D) 59.3 meters
7	Triangle PQR has angles measuring 23° and 48°. Which of the following could be the measure of an angle in a triangle similar to PQR and find the cosecant of the angle?	A) 0.852 B) 1.052 C) 1.452 D) 2.152
8	Solve for cos(2α) given that \$ sin(α) = - 5/13 \$ and \$ cos(α) = 12/13 \$ (α is in Quadrant II).	A) \$ 119/169 \$ B) \$ 129/159 \$ C) \$ 109/169 \$ D) \$ 119/139 \$
9	A kite is flying in the sky. The length of the string (hypotenuse) is 100 meters, and the kite makes an angle of 30 degrees with the ground. Determine the height of the kite above the ground using the quotient identities.	A) 20 m B) 50 m C) 40 m D) 30 m
10	Simplify the expression \$ (sin(x) cos(90^\circ - x) + cos(x) sin(90^\circ - x))/(tan(x) + cot(x) )\$.	A) \$ 2/(sec(3x))\$ B) \$(2csc(x))\$ C) \$ 1/(2csc(2x))\$ D) \$ 2/(3cot(2x))\$

Problem Id

Problem

Options

Find the exact value of sin(2θ) if \$ sin(θ) = 3/5 \$ and θ is in the first quadrant.

A) \$ 24/25 \$

B) \$ 23/27 \$

C) \$ 24/29 \$

D) \$ 21/28 \$

The two sides of the triangle x and y are 4 times shorter than the hypotenuse. Find the value of cos a?

A) \$ 3/4 \$

B) \$ 1/4 \$

C) \$ 2/3 \$

D) \$ 6/5 \$

A ladder is leaning against a wall. If the foot of the ladder is 5 meters away from the wall and the ladder is 10 meters long, find the angle the ladder makes with the ground.

A) 30°

B) 90°

C) 60°

D) 45°

Determine the value of cosec 150° using cofunction identities.

A) 1

B) 0

C) Undefined

D) 2

In a bridge construction project, an engineer needs to calculate the length of a diagonal brace connecting two beams. If one beam is 15 meters long and the angle between the brace and the horizontal beam is 30∘, find the length of the diagonal brace.

A) \$ 6\sqrt3 \$ meters

B) \$ 8\sqrt3 \$ meters

C) \$ 4\sqrt3 \$ meters

D) \$ 10\sqrt3 \$ meters

A person standing at point A observes the top of a tree at point T at an angle of elevation of 60 degrees. If the person walks 25 meters towards the tree to point B and observes the top of the tree at an angle of elevation of 75 degrees, calculate the height of the tree.

A) 34.25 meters

B) 38.25 meters

C) 43.3 meters

D) 59.3 meters

Triangle PQR has angles measuring 23° and 48°. Which of the following could be the measure of an angle in a triangle similar to PQR and find the cosecant of the angle?

A) 0.852

B) 1.052

C) 1.452

D) 2.152

Solve for cos(2α) given that \$ sin(α) = - 5/13 \$ and \$ cos(α) = 12/13 \$ (α is in Quadrant II).

A) \$ 119/169 \$

B) \$ 129/159 \$

C) \$ 109/169 \$

D) \$ 119/139 \$

A kite is flying in the sky. The length of the string (hypotenuse) is 100 meters, and the kite makes an angle of 30 degrees with the ground. Determine the height of the kite above the ground using the quotient identities.

A) 20 m

B) 50 m

C) 40 m

D) 30 m

Simplify the expression \$ (sin(x) cos(90^\circ - x) + cos(x) sin(90^\circ - x))/(tan(x) + cot(x) )\$.

A) \$ 2/(sec(3x))\$

B) \$(2csc(x))\$

C) \$ 1/(2csc(2x))\$

D) \$ 2/(3cot(2x))\$