Questions from Homework??

Find the missing measures. Write all answers in radical form. Warm – up Find the missing measures. Write all answers in radical form. 30° 60° 10 z y 3 45 y 60 30 x z

The Trigonometric Functions SINE Pronounced like “sign” COSINE Pronounced like “co-sign” TANGENT Pronounced “tan-gent”

With Respect to angle A, label the three sides Hypotenuse Opposite A C Adjacent

Let's see if you've got it! B With Respect to angle B, give each ratio using X, Y and Z. Z Y A C X 5

History of Trig Ratios A young brave, frustrated by his inability to understand the geometric constructions of his tribe's battle dress, kicked out in anger against a stone and crushed his big toe. Fortunately, he learned from this experience, and went on to become the greatest man in the tribe. However, because he was troubled throughout his life by the problematic toe he acquired in his youthful fit, he was constantly at the edge of the river, soaking his big toe in the cooling waters. For that behavior, he was named … Chief Soh Cah Toa.

Now the Chief is famous for his discoveries.

His name lives on to help us remember our ratios. SOH CAH TOA

10.8 9 6 Find the sine, the cosine, and the tangent of M. Give a fraction and decimal answer (round to 4 places). N 10.8 9 P 6 M

Find the sine, cosine, and the tangent of angle A 24.5 8.2 B C 23.1 Give a fraction and decimal answer. Round to 4 decimal places

sin ) 38 Using a Calculator to Find Values of Trig Functions You can simply use the sin, cos and tan buttons on the calculator followed by the degree measure of the angle. Sin (38º) sin ) 38 Use your mode button to change to degrees A word to the wise: Always make sure your calculator is in the right mode for the type of angle you have (degrees or radians)

Ex: 1 Find x. Round to the nearest tenth. 20 m x Figure out which ratio to use. What we’re looking for… What we know… adj opp

Ex: 2 Find the missing side. Round to the nearest tenth.

Ex: 3 Find the missing side. Round to the nearest tenth.

Ex: 4 Find the missing side. Round to the nearest tenth.

Find the height h of the lamppost to the nearest inch.

Ex. 5 A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? 200 60° x

Ex: 6 A surveyor is standing 50 metres from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? ? 71.5° 50 m

For some applications of trig, we need to know these meanings: angle of elevation and angle of depression.

Angle of Elevation Angle of Elevation If an observer looks UPWARD toward an object, the angle the line of sight makes with the horizontal. Angle of elevation

Angle of Depression If an observer looks DOWNWARD toward an object, the angle the line of sight makes with the horizontal. Angle of depression

You are skiing on a mountain with an altitude of 1200 meters You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21o. About how far do you ski down the mountain? ANSWER You ski about 3348 meters down the mountain.

You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp. ANSWER The height is about 6.1 feet.

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