What degrees is Angle c

How long does it take a cheetah to run 10 miles at 30 miles/hr?

quester [9]

20 minutes 60minutes ÷ 30miles = 20minutes

7 0

3 years ago

Which value of x solves the equation cos x° = sin (20° + x°), where 0 < x < 90? A. 30° B. 35° C. 40° D. 45° E. 55°

daser333 [38]

Answer:

Option B (35°).

Step-by-step explanation:

To solve this question, the trigonometric identity sin x = cos (90-x) is required. It can also be written as cos x = sin (90-x). It can be seen that this identity holds when the two angles are complementary i.e. they sum up to 90 degrees. Therefore, the answer can be determined by substituting all the options one by one in the identity cos x = sin (20+x). If x=30 degrees, then x+20=50 degrees. 30 and 50 are not complementary. If x=35 degrees, then x+20=55 degrees. 35 and 55 are complementary since their sum is 90 degrees. Therefore, B is the correct choice!!!

4 0

3 years ago

This is a map of three towns. It shows the train line and the highway that connects the towns. The north direction is shown. The

vlada-n [284]

Answer:

about 106 km

Step-by-step explanation:

The distance between the two towns can be estimated several ways. In the attachment, we chose to measure the angles on the map. Using the law of sines, we can estimate the unknown distance.

The distance can also be estimated using the Tounouse-Avaria distance as a ruler. For best results, that ruler would need to be subdivided to an appropriate level.

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<h3>angle measures</h3>

The angles in the triangle can be measured using a protractor or some other tool. The attachment shows the results from a geometry program:

∠TMA ≈ 107°
∠TAM ≈ 24°

<h3>law of sines</h3>

The law of sines tells us the distances are proportional to the sines of the opposite angles:

TM/sin(TAM) = TA/sin(TMA)

TM = sin(24°)×(250 km)/sin(107°) ≈ 106.3 km

The distance from Tounouse to Mt. Monotti is estimated to be about 106 km.

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<em>Alternate solution</em>

Using a compass or dividers to project the TM distance onto TA, we find it is between 0.4 and 0.5 of the TA distance. The difference between 2×TM and TA can be estimated to be about 0.4×TM. That is, ...

TM ≈ TA/2.4 ≈ (250 km)/2.4 ≈ 104.2 km

This estimate is consistent with the one found using angle measures.