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Kamila [148]
3 years ago
9

Use the given information to determine the exact trigonometric value. (in the image attached)

Mathematics
1 answer:
notka56 [123]3 years ago
6 0

Answer:

OPTION B: $ \frac{-2\sqrt{5}}{5} $

Step-by-step explanation:

Given $ cot \theta = -\frac{\sqrt{5}}{2} $

We know that, $ \frac{1}{cot \theta} = tan \theta $

$ \implies tan \theta = \frac{1}{-\frac{\sqrt{5}}{2}} $

$ = -\frac{2}{\sqrt{5}} $

Multiplying and dividing by $ \sqrt{5} $, we get:

$ tan \theta = - \frac{2 \sqrt{5}}{\sqrt{5}\times \sqrt{5}}} $

$ \implies tan \theta = -\frac{2\sqrt{5}}{5} $

Hence, OPTION B is the answer.

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10. 10. If AB bisects CAF, and m&lt;EAF = 72°,<br>then the m&lt;BAF =​
never [62]

The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

m∠EAF = 72° and AB bisects ∠CAF.

∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

∠DAC ≅ ∠EAF

m∠DAC = 72°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠DAE + m∠EAF = 180°

m∠DAE + 72° = 180°

Subtract 72° from both sides.

m∠DAE = 108°

∠CAF and ∠DAE are vertically opposite angles.

⇒ m∠CAF = m∠DAE

⇒ m∠CAF = 108°

AB bisects ∠CAF means ∠CAB = ∠BAF

m∠CAB + m∠BAF = 108°

m∠BAF + m∠BAF = 108°

2 m∠BAF = 108°

Divide by 2 on both sides, we get

m∠BAF = 54°

Hence the measure of ∠BAF is 54°.

4 0
3 years ago
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