Question

If tan α = 1/√3 and sin β = 1/√2 , find α + β.

Grade 10

Answer 1

a = alpha
b = beta

Tan a = 1/root3
= a is 30 degree (tan 30 = 1/root3)

sin b = 1/root2
= b is 45 degree (sin 45 = 1/root2)

So
a+b = 30 + 45 = 75

Ans. 75

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Answer 2

Given:

$\sf \large \: \circ \: \: \: Tan\:\alpha=\frac{1}{ \sqrt{3} } \\ \\ \large \sf\circ \: \: \: Sin \beta = \frac{1}{ \sqrt{2} }$

To find:

$\sf \large \circ \: \: \: \: \bold\alpha+\beta$

Solution:

$\large \sf \: Tan \: \alpha = \frac{1}{ \sqrt{3} } \\ \\ \sf \large as \: we \: know \: that \: tan \: 30 \degree = \frac{1}{ \sqrt{3} } \\ \\ \large\sf \large \underline{ \boxed{ \sf \pink{ so \: \angle \: \alpha = 30 \degree}}}$

$\sf \large \: Sin \: \beta= \frac{1}{ \sqrt{2} } \\ \\ \sf \large as \: we \: know \: that \: sin \: 45 \degree = \frac{1}{ \sqrt{2} } \\ \\ \sf \large \underline{ \boxed{ \sf \red{hence \: \beta = 45 \degree}}}$

$\sf \large \alpha + \beta \\ \\ \sf \large 30 \degree + 45 \degree \\ \\ \large \underline{ \boxed{ \sf \blue{ \implies75 \degree}}}$