Question

1. multiple choice on which of the following triangles can the pythagorean theorem be used? remember that the sum of the angles of a triangle is 180°. applying the mathematics 10. a rectangular farm is pictured below. it is 10.8 kilometers long and 4.5 kilometers wide. angelina wants to go from point a to point b. a. what is the distance if angelina goes along the roads that surround the farm? b. what is the distance if angelina goes by tractor along the diagonal of the farm? c. how much shorter is it to go through the farm than to go along the roads?

Explanation:

Step1: Recall Pythagorean - Theorem condition

The Pythagorean Theorem $a^{2}+b^{2}=c^{2}$ is used for right - angled triangles (triangles with one angle equal to $90^{\circ}$).

Step2: Check angles of each triangle in question 9

• In triangle A, one angle is $120^{\circ}$, not a right - angled triangle.
• In triangle B, $55^{\circ}+35^{\circ}=90^{\circ}$, so it is a right - angled triangle.
• In triangle C, $30^{\circ}+50^{\circ}=80^{\circ}

eq90^{\circ}$, not a right - angled triangle. So the answer to question 9 is B.

Step3: Solve question 10a

If Angelina goes along the roads, the distance $d_1$ is the sum of the length and the width of the rectangle. $d_1 = 10.8+4.5=15.3$ km.

Step4: Solve question 10b

For the diagonal of the rectangle, use the Pythagorean Theorem. Let the length $l = 10.8$ km and the width $w = 4.5$ km. The diagonal $d_2=\sqrt{l^{2}+w^{2}}=\sqrt{10.8^{2}+4.5^{2}}=\sqrt{116.64 + 20.25}=\sqrt{136.89}=11.7$ km.

Step5: Solve question 10c

Find the difference $\Delta d=d_1 - d_2=15.3−11.7 = 3.6$ km.

Answer:

1. B. A triangle with angles $55^{\circ},35^{\circ},90^{\circ}$

10a. 15.3 km
10b. 11.7 km
10c. 3.6 km