lesson 12.2 problem solving with right triangles

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Question: Lesson 12.2 Problem Solving with Right Triangles Name Period_ For Exercises 1-3, find the area of each figure to the nearest square unit. 3. Area 2. Area_ 1. Area_ For Exercises 4-9, find each unknown to the nearest tenth of a unit. 4. Area 88 cm2 17台 8. Right cone 9. Right rectangular prisnm 7. P3 and PT are tangents. Diameter 10 in. 24 in. 13 ft 4 in. 22

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To find the area of triangle , use the fact that and .

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12.2 Problem Solving with Right Triangle...

9th - 12th grade, mathematics.

12.2 Problem Solving with Right Triangles

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Round 1 decimal place.

A ladder 7m long, leaning against a vertical wall makes an angle of 60 degrees with the ground. How high on the wall does the ladder reach? Round 2 decimal places.

Find the area of the Kite. Round to the nearest whole number.

Find the area of the regular pentagon if s = 12 cm.

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Right Triangles

Rules, Formula and more

Pythagorean Theorem

The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse .

Usually, this theorem is expressed as $$ A^2 + B^2 = C^2 $$ .

Right Triangle Properties

A right triangle has one $$ 90^{\circ} $$ angle ($$ \angle $$ B in the picture on the left) and a variety of often-studied formulas such as:

• The Pythagorean Theorem
• Trigonometry Ratios (SOHCAHTOA)
• Pythagorean Theorem vs Sohcahtoa (which to use)

SOHCAHTOA only applies to right triangles ( more here ) .

A Right Triangle's Hypotenuse

The hypotenuse is the largest side in a right triangle and is always opposite the right angle.

In the triangle above, the hypotenuse is the side AB which is opposite the right angle, $$ \angle C $$.

Online tool calculates the hypotenuse (or a leg) using the Pythagorean theorem.

Practice Problems

Below are several practice problems involving the Pythagorean theorem, you can also get more detailed lesson on how to use the Pythagorean theorem here .

Find the length of side t in the triangle on the left.

Substitute the two known sides into the Pythagorean theorem's formula : A² + B² = C²

What is the value of x in the picture on the left?

Set up the Pythagorean Theorem : 14 2 + 48 2 = x 2 2,500 = X 2

$$ x = \sqrt{2500} = 50 $$

$$ x^2 = 21^2 + 72^2 \\ x^2= 5625 \\ x = \sqrt{5625} \\ x =75 $$

Find the length of side X in the triangle on on the left?

Substitue the two known sides into the pythagorean theorem's formula : $$ A^2 + B^2 = C^2 \\ 8^2 + 6^2 = x^2 \\ x = \sqrt{100}=10 $$

What is x in the triangle on the left?

x 2 + 4 2 = 5 2 x 2 + 16 = 25 x 2 = 25 - 16 = 9 x = 3

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