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2 years ago

If EBC = 31a - 2 and EBH = 4a + 45 find HBC

Mathematics

1 answer:

Zigmanuir [339]2 years ago

8 0

Answer:

The measure of angle HBC is m∠HBC=61°

Step-by-step explanation:

In this problem we have that

The line BH bisects angle EBC,

see the attached figure to better understand the problem

then

m∠EBC=m∠EBH+m∠HBC

m∠EBH=m∠HBC

m∠EBC=2(m∠EBH)

substitute the given values and solve for a

$31a-2=2(4a+45)\\31a-2=8a+90\\31a-8a=92\\23a=92\\a=4$

<em>Find the measure of angle EBH</em>

m∠EBH=(4(4)+45)=61°

Remember that

m∠EBH=m∠HBC

therefore

The measure of angle HBC is m∠HBC=61°

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2 years ago

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Answer:

The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.

Step-by-step explanation:

It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.

Let the acute angle be m∠A.

For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.

The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,

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So for acute angle 45° the ratio of Sin 45° and Cos 45° is:

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