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Mrac [35]
4 years ago
5

Find C and D using formula for special right triangles

Mathematics
1 answer:
Anuta_ua [19.1K]4 years ago
6 0

Given:

Right triangles:

To find:

The value of c and value of d

Solution:

<u>In the first right triangle:</u>

θ = 45°

Opposite side to θ = 5

Hypotenuse = c

$\sin \theta=\frac{\text { Opposite side of } \theta}{\text { Hypotenuse }}

$\sin 45^\circ=\frac{5}{c}

The value of sin 45° = \frac{1}{\sqrt 2}

$\frac{1}{\sqrt 2}=\frac{5}{c}

Do cross multiplication, we get

c=5\sqrt{2}

<u>In the second right triangle:</u>

θ = 60°

Opposite side to θ = 4

Adjacent side to θ = d

$\tan \theta=\frac{\text { Opposite side of } \theta}{\text  { Adjacent side of } \theta}

$\tan 60^\circ=\frac{4}{d}

$\sqrt{3} =\frac{4}{d}

Do cross multiplication, we get

$d=\frac{4}{\sqrt{3} }

The value of c=5\sqrt{2} and d=\frac{4}{\sqrt{3} }.

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