Question

In right triangle ABC, m∠A = 30° and m∠B = 90°. Which of the following are true?

I. sin(A) = sin(C)
II. sin(A) = cos(C)
III. cos(A) = cos(C)
IV. cos(A) = sin(C)
A.
II and IV
B.
I and III
C.
I and II
D.
III and IV

Answer 1

Answer:

II and IV

Explanation: Plato

Step-by-step explanation:

Answer 2

In the right triangle ABC, $m\angle A = 30$°, and $m\angle B = 60$ then, $sin(A) = cos(C)$ and $cos(A) = sin(C)$.

What is a triangle?

" Triangle is defined as the two-dimensional closed shape with three vertices, three sides, and three angles enclosed in it."

According to the question,

In the  right triangle ABC,

As we know,

$m\angle A +m\angle B +m\angle C = 180\°$

Given,

$m\angle A = 30$°,

$m\angle B = 60$°

Therefore in the right triangle ABC,

$m\angle C = 180 - ( 90+30)\\\\m\angle C = 60\°$

Now find the value of the required trigonometric function we get,

$sin(30\°) = \frac{1}{2}$

$sin(60\°) = \frac{\sqrt{3} }{2}$

$cos(30\°) = \frac{\sqrt{3} }{2}$

$cos(60\°) = \frac{1}{2}$

Therefore,

$sin(30\°) = cos (60\°) \implies sin(A) = cos(C)\\\\sin(60\°) = cos (30\°)\implies cos(A) = sin(C)$

Hence, Option(A) is the correct answer.

Learn more about triangles here

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