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Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
[Case Study]
A gardener is laying out a triangular flower bed in the shape of a right triangle, as shown, with the right angle at the corner where two straight edges of the bed meet. The two straight edges measure $6$ m and $8$ m, and the sloped edge (hypotenuse) measures $10$ m. The angle marked $\theta$ is at one corner of the bed.
(a) Find $\sin\theta$. [1 Mark]
(b) Find $\cos\theta$. [1 Mark]
(c) Verify that $\sin^2\theta+\cos^2\theta=1$ for this triangle. [1 Mark]
(d) Find $\tan\theta$. [1 Mark]
A gardener is laying out a triangular flower bed in the shape of a right triangle, as shown, with the right angle at the corner where two straight edges of the bed meet. The two straight edges measure $6$ m and $8$ m, and the sloped edge (hypotenuse) measures $10$ m. The angle marked $\theta$ is at one corner of the bed.
(a) Find $\sin\theta$. [1 Mark]
(b) Find $\cos\theta$. [1 Mark]
(c) Verify that $\sin^2\theta+\cos^2\theta=1$ for this triangle. [1 Mark]
(d) Find $\tan\theta$. [1 Mark]
Step-by-Step Solution
Key Concept: Case study on trigonometry ratios and identities.
(a) Find $\sin\theta$. [1 Mark]
$\sin\theta=\dfrac{6}{10}=\dfrac35$. [1.0 Mark]
(b) Find $\cos\theta$. [1 Mark]
$\cos\theta=\dfrac{8}{10}=\dfrac45$. [1.0 Mark]
(c) Verify that $\sin^2\theta+\cos^2\theta=1$ for this triangle. [1 Mark]
$\left(\dfrac35\right)^2+\left(\dfrac45\right)^2=\dfrac{9}{25}+\dfrac{16}{25}=\dfrac{25}{25}=1$. Verified. [1.0 Mark]
(d) Find $\tan\theta$. [1 Mark]
$\tan\theta=\dfrac{6}{8}=\dfrac34$. [1.0 Mark]
$\sin\theta=\dfrac{6}{10}=\dfrac35$. [1.0 Mark]
(b) Find $\cos\theta$. [1 Mark]
$\cos\theta=\dfrac{8}{10}=\dfrac45$. [1.0 Mark]
(c) Verify that $\sin^2\theta+\cos^2\theta=1$ for this triangle. [1 Mark]
$\left(\dfrac35\right)^2+\left(\dfrac45\right)^2=\dfrac{9}{25}+\dfrac{16}{25}=\dfrac{25}{25}=1$. Verified. [1.0 Mark]
(d) Find $\tan\theta$. [1 Mark]
$\tan\theta=\dfrac{6}{8}=\dfrac34$. [1.0 Mark]
Correct Answer: $\sin\theta=\dfrac{6}{10}=\dfrac35$. [1.0 Mark] | $\cos\theta=\dfrac{8}{10}=\dfrac45$. [1.0 Mark] | $\left(\dfrac35\right)^2+\left(\dfrac45\right)^2=\dfrac{9}{25}+\dfrac{16}{25}=\dfrac{25}{25}=1$. Verified. [1.0 Mark] | $\tan\theta=\dfrac{6}{8}=\dfrac34$. [1.0 Mark]
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