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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Trigonometry ratios in right triangles

Grade: 10-a Lesson: S3-L2

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	In the given figure, PO: OQ = 6:8 and perimeter of △POQ = 96 m. Determine OP, QR, and QP. $1$	A)OP = 40 m , PQ = 24 m and QP = 64 m B) OP = 24 m , RQ = 64 m and QP = 40 m C) OP = 40 m , RQ = 64 m and QP = 24 m D) OP = 64 m , RQ = 24 m and QP = 40 m
2	Consider △ACB, right-angled at C, in which AB = 21 in, BC = 20 in, and ∠ABC = \$ \theta \$ (see fig). Determine the values of \$ cos^2 \theta - sin^2 \theta \$. $2$	A) -2 B) -1 C) 2 D) 1
3	In a triangle DEF, right-angled at E , DE = 23 in and angle \$D = 45^o\$. Find the CosD. $3$	A) \$- 1/\sqrt2\$ B) \$-\sqrt2\$ C) \$\sqrt2\$ D) \$1/\sqrt2\$
4	In △MNO, right-angled at N, ON = 7 m, and MO − MN = 5 m, and determine the values of 2sinO + 2cosO. $4$	A) \$-94/37\$ B)\$37/94\$ C) \$-37/94\$ D) \$ 94/37\$
5	In ∆ ABC, right angled at B, if tan A = \$3/\sqrt4 \$ then the value of 2sin A + 2cos A.	A) \$-(10\sqrt(13))/(13)\$ B) \$(11\sqrt(13))/(13)\$ C) \$(10\sqrt(13))/(13)\$ D) \$-(11\sqrt(13))/(13)\$
6	In the given figure, PO: OQ = 3: 4 and perimeter of △POQ = 72 cm. Determine OP, QR, and QP. $6$	A) OP = 30cm, QR = 18cm , QP = 48 cm B) OP = 30cm, QR = 48cm , QP = 18 cm C) OP = 18cm, QR = 48cm , QP = 30 cm D) OP = 18cm, QR = 30cm , QP = 48 cm
7	In a right triangle CBA with a right angle at B, where a = 4 units and b = 3 units, find cos \$\theta\$ and tan \$\theta\$ of angle CBA. $7$	A) \$4/5, 3/4\$ B) \$3/5, 7/2\$ C) \$5/7, 4/3\$ D) \$3/5, 4/3\$
8	Consider △ACB, right-angled at C, in which AB = 31 units, BC = 22 units, and ∠ACB = \$ \theta \$ (see fig). Determine the values of \$ sin^2 \theta + cos^2 \theta \$. $8$	A) 1 B) 0 C) \$477/31\$ D) \$31/477\$
9	Given \$cot \theta = 3/4 \$, find the other trigonometric ratios of the angle \$\theta\$.	A) \$sin \theta = 3/5, cos \theta = 3/4, tan \theta = 4/3 \$, \$csc \theta = 5/4, sec \theta = 4/3\$ B) \$sin \theta = 4/5, cos \theta = 3/5, tan \theta = 4/3 \$, \$csc \theta = 5/4, sec \theta = 4/3\$ C) \$sin \theta = 5/3, cos \theta = 3/5, tan \theta = 4/3 \$, \$csc \theta = 5/4, sec \theta = 4/3\$ D) \$sin \theta = 4/5, cos \theta = 3/4, tan \theta = 4/3 \$, \$csc \theta = 6/4, sec \theta = 4/3\$
10	Triangle XYZ is a right triangle with a right angle at Y. XZ (hypotenuse) has a length of 10 cm and XY is 6 cm. A circle is drawn with T as the center and TY as the radius. What is the length of the chord of this circle passing through Y and Z? $10$	A) 7 B) 8 C) 9 D) 10

Problem Id

Problem

Options

In the given figure, PO: OQ = 6:8 and perimeter of △POQ = 96 m. Determine OP, QR, and QP.

$1$

A)OP = 40 m , PQ = 24 m and QP = 64 m

B) OP = 24 m , RQ = 64 m and QP = 40 m

C) OP = 40 m , RQ = 64 m and QP = 24 m

D) OP = 64 m , RQ = 24 m and QP = 40 m

Consider △ACB, right-angled at C, in which AB = 21 in, BC = 20 in, and ∠ABC = \$ \theta \$ (see fig). Determine the values of \$ cos^2 \theta - sin^2 \theta \$.

$2$

A) -2

B) -1

C) 2

D) 1

In a triangle DEF, right-angled at E , DE = 23 in and angle \$D = 45^o\$. Find the CosD.

$3$

A) \$- 1/\sqrt2\$

B) \$-\sqrt2\$

C) \$\sqrt2\$

D) \$1/\sqrt2\$

In △MNO, right-angled at N, ON = 7 m, and MO − MN = 5 m, and determine the values of 2sinO + 2cosO.

$4$

A) \$-94/37\$

B)\$37/94\$

C) \$-37/94\$

D) \$ 94/37\$

In ∆ ABC, right angled at B, if tan A = \$3/\sqrt4 \$ then the value of
2sin A + 2cos A.

A) \$-(10\sqrt(13))/(13)\$

B) \$(11\sqrt(13))/(13)\$

C) \$(10\sqrt(13))/(13)\$

D) \$-(11\sqrt(13))/(13)\$

In the given figure, PO: OQ = 3: 4 and perimeter of △POQ = 72 cm. Determine OP, QR, and QP.

$6$

A) OP = 30cm, QR = 18cm , QP = 48 cm

B) OP = 30cm, QR = 48cm , QP = 18 cm

C) OP = 18cm, QR = 48cm , QP = 30 cm

D) OP = 18cm, QR = 30cm , QP = 48 cm

In a right triangle CBA with a right angle at B, where a = 4 units and b = 3 units, find cos \$\theta\$ and tan \$\theta\$ of angle CBA.

$7$

A) \$4/5, 3/4\$

B) \$3/5, 7/2\$

C) \$5/7, 4/3\$

D) \$3/5, 4/3\$

Consider △ACB, right-angled at C, in which AB = 31 units, BC = 22 units, and ∠ACB = \$ \theta \$ (see fig). Determine the values of \$ sin^2 \theta + cos^2 \theta \$.

$8$

A) 1

B) 0

C) \$477/31\$

D) \$31/477\$

Given \$cot \theta = 3/4 \$, find the other trigonometric ratios of the angle \$\theta\$.

A) \$sin \theta = 3/5, cos \theta = 3/4, tan \theta = 4/3 \$, \$csc \theta = 5/4, sec \theta = 4/3\$

B) \$sin \theta = 4/5, cos \theta = 3/5, tan \theta = 4/3 \$, \$csc \theta = 5/4, sec \theta = 4/3\$

C) \$sin \theta = 5/3, cos \theta = 3/5, tan \theta = 4/3 \$, \$csc \theta = 5/4, sec \theta = 4/3\$

D) \$sin \theta = 4/5, cos \theta = 3/4, tan \theta = 4/3 \$, \$csc \theta = 6/4, sec \theta = 4/3\$

Triangle XYZ is a right triangle with a right angle at Y. XZ (hypotenuse) has a length of 10 cm and XY is 6 cm. A circle is drawn with T as the center and TY as the radius. What is the length of the chord of this circle passing through Y and Z?

$10$

A) 7

B) 8

C) 9

D) 10