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oksian1 [2.3K]
3 years ago
10

An equilateral triangle LMQ is drawn

Mathematics
1 answer:
Bogdan [553]3 years ago
5 0

The measure of the ∠LQP is 120°

Step-by-step explanation:

The diagram of the question is as attached in the image.

LMNP is a square. We know that for a square all sides are equal and intersects at 90°

Hence, LM=MP=PN=LN

and ∠LMP= ∠MPN= ∠PNL= ∠NLM= 90°

Δ LMQ is an equilateral triangle

We know that for equilateral triangle all sides are equal and all angles are 60°

LM=LQ=QM=MP=PN=LN and

∠LQM= ∠QML= ∠MLQ= 60°

∠LQP= ∠LQM+ ∠MQP   eq 1

In Δ MPQ

∠QPM=90° and ∠PMQ= 90°-60°=30°

Hence, ∠MQP= 180°-(90°+30°)=60°

Putting the value of ∠MQP and ∠LQM in equation 1

∠LQP= 60°+60°= 120°

Thus the measure of ∠LQP=120°

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<u>Step-by-step explanation:</u>

Given data:

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3 years ago
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Step-by-step explanation:

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Step-by-step explanation:

Part A) Find sin(\alpha)\ and\ cos(\beta)

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

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sin(\alpha)=\frac{4}{7}

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Part B) Find tan(\alpha)\ and\ cot(\beta)

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

tan(\alpha)=cot(\beta)

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132

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x=2\sqrt{33}\ units

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we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

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sec(\alpha)=\frac{1}{cos(\alpha)}

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cos(\alpha)=\frac{2\sqrt{33}}{14} ---> adjacent side divided by the hypotenuse

simplify

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therefore

sec(\alpha)=\frac{7}{\sqrt{33}}

csc(\beta)=\frac{7}{\sqrt{33}}

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Step-by-step explanation:

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