Answer:
Step-by-step explanation:
You can observe in the figure two parallel lines that are intersected by a transversal and several angles are formed.
The angles m∠3 and m∠6 are located inside the parallel lines and on one side of the transversal, this angles are known as "Consecutive interior angles" and they are supplementary (which means that they add up 180°).
Therefore, you know that:
So you can substitute m∠3=130° and solve for m∠6. Then you get:
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:
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.
