Question

asked Feb 7, 2022 87.4k views

1 Answer

Caulfield · Answer 1 · 2022-02-11T16:42:19+0000

Answer:

c = 3.6

$A = 56.4^\circ$

$B = 33.6^\circ$

Explanation:

Given

See attachment

Solving (a): Segment C

To do this, we make use of Pythagoras theorem

c^2 =a^2 + b^2

c^2 =2^2 + 3^2

c^2 = 4 + 9

c^2 = 13

Take the square root of both sides

$c = \sqrt{13$

c = 3.6055

c = 3.6 --- Approximate

Solving (b): Measure of A

To do this, we make use of:

$sin\ A = (Opposite)/(Hypotenuse)$

This gives:

$sin\ A = (3)/(3.6)$

$sin\ A = 0.8333$

Take arcsin of both sides

A = sin^(-1)(0.8333)

$A = 56.4^\circ$

Solving (c): The measure of C

This is calculated as:

$A + B + 90^\circ = 180^\circ$

So, we have:

$B = 180^\circ - 90^\circ - 56.4^\circ$

$B = 33.6^\circ$

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