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Kruka [31]
3 years ago
10

Which triangle can be drawn as it is described?

Mathematics
1 answer:
yawa3891 [41]3 years ago
8 0

Answer:

An isosceles triangle with angles measuring 20° and 80°

Step-by-step explanation:

Verify each case

case A) Scalene triangle with angles measuring 110° and 35°

Is not a scalene triangle because the third angle is (180-110°-35°=35°), therefore is an isosceles triangle

case B) An obtuse triangle with sides measuring 5,10 and 15

we know that

Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so in this problem

5+10> 15 -----> is not true

therefore

with these measurements can not draw any triangle

case C) An isosceles triangle with angles measuring 20° and 80°

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem the third angle is (180-20°-80°=80°),

therefore

is an isosceles triangle and can be drawn as it is described

case D) An acute triangle with sides measuring 7,4 and 2

we know that

Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so in this problem

4+2> 7 -----> is not true

therefore

with these measurements can not draw any triangle

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_____

<em>Comment on the problem</em>

We suspect that the angle is supposed to be considered to be 90°. However, the given angle is reported to 2 decimal places, so we figure the requested angle should also be reported to 2 decimal places.

The lengths of the short side that correspond to the above angles are 10.03 and 9.97 units. If the short side were considered to be 10 units, the triangle would be a right triangle, and the larger acute angle would be ...

  arcsin(24/26) ≈ 67.38014° . . . . rounds to 67.38°

This points up the difficulty of trying to use the Law of Sines on a triangle that is actually a right triangle.

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