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2 years ago

Evaluate the diagram below. Find the measures of Angles A, B, C, and D.

Mathematics

1 answer:

laiz [17]2 years ago

5 0

Answer:

A: 65° B: 65° C: 125° D: 125°

Step-by-step explanation:

It is an equilateral(shown by the two dashes) and all angles in a triangle add up to 180°.

180-50 divided by 2 to give you A and B angles.

Then angled on a straight line add up to 180° so if you take angle A away from 180° you will get the answer to angle C.

The same for angle D.

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What is 6/10 fraction as decimal

dexar [7]

I am pertty sure its 0.6 but if i am wrong sorry

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2 years ago

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The angle looking up at the sun is 70°. A flagpole casts a shadow of 15 ft. Draw a diagram and find the height of the flagpole

deff fn [24]

Answer:

The length of the flagpole be 41.2 ft .

Option (A) is correct .

Step-by-step explanation:

As given

The angle looking up at the sun is 70°.

A flagpole casts a shadow of 15 ft .

Now by using the trignometric identity .

$tan \theta = \frac{Perpendicular}{Base}$

$\ theta = 70^{\circ}$

$tan\ 70^{\circ} = \frac{AB}{BC}$

BC = 15 ft

tan 70° = 2.75 (Approx)

$2.75 = \frac{AB}{15}$

AB = 2.75 × 15

= 41.2 ft

Therefore the length of the flagpole be 41.2 ft .

Option (A) is correct .

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3 years ago

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What expression represents the phrase eight less than the product of a number and two

JulijaS [17]

Answer:

Step-by-step explanation:

eight less then the product of a number and 2

" the product " means multiply

the product of a number and 2.......2x

eight less....-8

2x - 8 <=== ur expression

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2 years ago

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We need to attach a support wire to Glendale's flagpole, which is 24 feet high. The

antoniya [11.8K]

Step-by-step explanation:

this creates a right-angled triangle.

the right angle (90°) being the angle between flag pole and ground.

the angle ground-wire is 50°.

because we know that the sum of all angles in a triangle is always 180°, we know then that the angle flagpole-wire is

180 - 90 - 50 = 40°

so, we have the situation to know 1 side and all angles.

to get the other sides we use best the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and related angles are always opposite of each other.

in our case now we have

24/sin(50) = wire/sin(90) = wire/1 = wire = 31.32977494... ft

so, the rounded answer is that the wire must be

31.3 ft long

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2 years ago

(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this

Xelga [282]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

$\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta$

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

$\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta$

Simplify. The denominator uses the difference of two squares pattern:

$\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta$

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

$\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta$

Split into two separate fractions:

$\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta$

Rewrite the two fractions:

$\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta$

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

$\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta$

Hence verified.

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2 years ago