 #  In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs  a 2 + b 2 = c 2 a, leg.

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 In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs  a 2 + b 2 = c 2 a, leg b, leg c, hypotenuse

 a set of 3 positive integers a, b, and c that satisfy the equation a 2 + b 2 = c 2.  3,4,55,12,138,15,177,24,25 and multiples of these numbers like….  6,8,1010,24,2616,30,3414,48,50

 A ramp for a truck is 6 feet long. The bed of the truck is 3 feet above the ground. How long is the base of the ramp?

 If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.  If c 2 = a 2 + b 2, then triangle ABC is a right triangle.

 If c 2 < a 2 + b 2, then the triangle is acute.  If c 2 > a 2 + b 2, then the triangle is obtuse.

GivenDiagram:

 GivenDiagram:

 Theorem - If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.  If CD is an altitude of ABC, then CBD ~ ABC ~ ACD

 Identify the similar triangles

 Side view of a tool shed  What is the maximum height of the shed to the nearest tenth?

 In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the length of the two segments

 In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

 Find K

 45 o -45 o -90 o Triangle Theorem- In a 45 o -45 o -90 o triangle, the hypotenuse is √ 2 times as long as each leg.

 In a 30 o -60 o -90 o triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is √ 3 times as long as the shorter leg.

 A logo in the shape of an equilateral triangle  Find the height of the logo.  Each side is 2.5 inches long.

 Trigonometric Ratio- a ratio of the lengths of two sides of a right triangle.  SOH – CAH- TOA

 Tangent- ratio of the length of the opposite leg to the adjacent leg of a right triangle (Round to 4 decimal places.)- “TOA”

 Find x. Round to the nearest tenth.

 Find the height of the flagpole to the nearest foot.

 Sine “SOH”  Cosine “CAH”

 Solve the right triangle formed by the water slide.

 Inverse tan tan -1  If tan A = x then, tan -1 x = m<A  Inverse sin sin -1  If sin A = y, then sin -1 y= m<A  Inverse cos cos -1  If cos A = z, then cos -1 z = m<A

 Angle C is an acute angle in a right triangle. Approximate the m<C is to the nearest tenth degree when:  Sin C = 0.2400  Cos C = 0.3700

 Approximate the measure of angle Q to the nearest tenth of a degree.

 A road rises 10 feet over a 200 foot horizontal distance. Find the angle of elevation.

 To solve a right triangle means to find the measures of all of the sides and angles.  You need:  2 side lengths or  one side and one angle

 Angle of Elevation- the angle your line of sight makes with a horizontal line while looking up  Angle of Depression- the angle your line of sight makes with a horizontal line while looking down

 You are skiing down a mountain with an altitude of 1200m. The angle of depression is 21 o. How far do you ski down the mountain? Round to the nearest meter.

 You are looking up at an airplane with an altitude of 10,000ft. Your angle of elevation is 29 o. How far is the plane from where you are standing? Round to the nearest foot.

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