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2 years ago

Find the value of x and the measure of the missing angle labeled A:

Mathematics

1 answer:

Nostrana [21]2 years ago

8 0

Answer:

x = -2

∠A = 35

Step-by-step explanation:

x + 37 + x + 57 = 90

reduce:

2x = -4

x = -2

∠A = 37-2 = 35

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Prove that tan 10+tan 70'+taniou = tanio tanfo'tam 1oo.

Galina-37 [17]

Question:

Prove that:

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$

Answer:

Proved

Step-by-step explanation:

Given

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$

Required

Prove

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$

Subtract tan(10) from both sides

$- tan(10)+tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)$

$tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)$

Factorize the right hand size

$tan(70) + tan(100) = -tan(10)(-tan(70). tan(100) + 1)$

Rewrite as:

$tan(70) + tan(100) = -tan(10)(1-tan(70). tan(100))$

Divide both sides by $1-tan(70). tan(100)$

$\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = \frac{-tan(10)(1-tan(70). tan(100))}{1-tan(70). tan(100))}$

$\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10)$

In trigonometry:

$tan(A + B) = \frac{tan(A) + tan(B)}{1 - tan(A)tan(B)}$

So:

$\frac{tan(70) + tan(100)}{1 - tan(70)tan(100)}$ can be expressed as: $tan(70 + 100)$

$\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10)$ gives

$tan(70 + 100) = -tan(10)$

$tan(170) = -tan(10)$

In trigonometry:

$tan(180 - \theta) = -tan(\theta)$

So:

$tan(180 - 10) = -tan(10)$

Because RHS = LHS

Then:

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$ has been proven

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3 years ago

If the measure of central angle is 57 degrees, what is the measure of its intercepted arc? (just write the number, no degrees)

____ [38]

If a central angle measures 57 degrees, based on the angle-arc relationship, the measure of its intercepted arc = 57 degrees.

<em><u>Recall:</u></em>

The image attached below shows the relationship between the measure of the central angle and its intercepted arc.

Measure of central angle = its intercepted arc.

Thus, if the measure of a central angle = 57 degrees, based on the angle-arc relationship, the measure of its intercepted arc will also be 57 degrees.

Learn more about central angles on:

brainly.com/question/2548029

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2 years ago