Evaluate the expression 7x^2y when x = 3 and y + 4 six grade math
1 answer:
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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°
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.
Answer:
The correct answer is 61.08 foot.
Step-by-step explanation:
Length of the string of the kite, Mr. Black is flying is 65 foot. Thus the length between the kite and Mr. Black is given by 65 foot.
Angle of elevation is 70°.
We need to calculate the height of the kite above Mr. Black's head. The height is given by finding the sine of the angle of elevation.
Let the height be x foot.
Thus sin 70° =
⇒ x = sin 70° × 65
⇒ x = 61.08
Thus the height of the kite above Mr. Black head is 61.08 foot.