Amazing Mathematics Finding Unknown Measures In Similar Triangles Answers

FINDING MISSING MEASURES IN SIMILAR TRIANGLES WORKSHEET

Problem 1 :

While playing tennis, David is 12 meters from the net, which is 0.9 meter high. He needs to hit the ball so that it just clears the net and lands 6 meters beyond the base of the net. At what height should Matt hit the tennis ball ?

Problem 2 :

Jose is building a wheelchair ramp that is 24 feet long and 2 feet high. She needs to install a vertical support piece 8 feet from the end of the ramp. What is the length of the support piece in inches ?

Detailed Answer Key

Problem 1 :

Solution :

Step 1 :

Draw an appropriate diagram to the given information

In the above diagram,

BC = Height of the net

DE = Height of ball when hit

A = Point at where the ball lands

Step 2 :

Let us compare two corresponding angles of triangle ABC and ADE.

Triangle ABC

m ∠A (Common angle)

m ∠B (Right angle)

Triangle ADE

m ∠A (Common angle)

m ∠D (Right angle)

Because two angles in one triangle are congruent to two angles in the other triangle, the two triangles are similar.

Step 3 :

Since the triangle ABC and ADE are similar triangles, corresponding side lengths are proportional.

So, we have

AD / DB = DE / BC

(AB + BD) / DB = DE / BC

Substitute the lengths from the figure.

(6 + 12) / 6 = h / 0.9

18 / 6 = h / 0.9

3 = h / 0.9

Multiply both sides by 0.9

3⋅ 0.9 = (h/0.9) ⋅ 9

2.7 = h

So, David should hit the ball at a height of 2.7 meters.

Problem 2 :

Solution :

Step 1 :

Draw an appropriate diagram to the given information

In the above diagram,

AB = Height of the chair

CD = Height of the support piece

E = End of the ramp

Step 2 :

Let us compare two corresponding angles of triangle ABE and CDE.

Triangle ABE

m ∠E (Common angle)

m ∠B (Right angle)

Triangle ADE

m ∠E (Common angle)

m ∠D (Right angle)

Because two angles in one triangle are congruent to two angles in the other triangle, the two triangles are similar.

Step 3 :

Since the triangle ABE and ADE are similar triangles, corresponding side lengths are proportional.

So, we have

DE / BE = CD / AB

Substitute the lengths from the figure.

8 / 24 = h / 2

1 / 3 = h / 2

Multiply both sides by 2.

(1/3) ⋅ 2 = (h/2) ⋅ 2

2/3 ft = h

Step 4 :

Convert feet into inches.

Because 1 ft = 12 inches, we have to multiply by 12 to convert feet into inches.

h = 2/3 ft

h = (2/3) ⋅ 12 inches

h = 8 inches

So, the length of the support piece is 8 inches.

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