Plz help me well mark brainliest if correct...........???

Furkat [3]

<h3>Answer: Choice D) 31.2 miles</h3>

This value is approximate.

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Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

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To sum things up so far, we have these known properties of triangle ABC

angle A = 107 degrees
side c = side AB = 24 miles
angle B = 42 degrees
angle C = 31 degrees

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

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

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

8 0

2 years ago

Find the length of the third side. If necessary, write in simplest radical form.

Mazyrski [523]

Answer:

$\boxed {\boxed {\sf 8}}$

Step-by-step explanation:

This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.

$a^2+b^2=c^2$

Where <em>a</em> and <em>b </em> are the legs of the triangle and <em>c</em> is the hypotenuse.

In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:

$a= 7 \\b= \sqrt{15}$

Substitute these values into the formula.

$(7)^2+(\sqrt{15})^2=c^2$

Solve the exponents.

(7)²= 7*7=49

$49+ (\sqrt{15})^2=c^2$

(√15)²=√15*√15=15

$49+15=c^2$

Add.

$64=c^2$

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

$\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c$