## Alberta Free Tutoring And Homework Help For Math 10C

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### find the side length of the right triangle

#### Attached Whiteboard:

5 years ago cos(45) = ?/17

1/$\sqrt{2}$2 = ?/17

17/ $\sqrt{2}$2 = ?

5 years ago cos(45)= a/17

a=12.02 cm

Review Cos, Sin and Tan... then pretty easy to solve this.

5 years ago Let x be the ? side length.

cos 45 = x/17 (since 17 cm is the hypotenuse as it is opposite the right angle and the side x is adjacent to the angle 45 degree)

cos 45/1 = x/17

x = 17*cos 45 (using cross multiplication)

x = 12.02 cm

5 years ago This is a classical example of the Pythagorean Theorem. It states that in any right triangle, the sum of the squares of the lenght of the triangle legs is the same as the square of the lenght of the triangle.

Lets say that:

5 years ago $C^2=a^2+b^2$C2=a2+b2       We only know C=17 cm and the angle 45. So we need to remember that :

Sin Q = Op / Hyp  = b/c

Tan Q= a/b

In this case we have to take  Cos Q = a/c

Therefore : a = c x cos Q ; substituting the terms , we have  a = 17x cos 45 = 17x 0.707=12.02 cm

Finally we have the answer , a = 12.02 cm

5 years ago Remember that Cos( $\theta$θ ) = adj/hyp.

So in this case we need to solve the following equation;

Cos(45) = x/17

17Cos(45) = x     [Multiply both sides by 17]

Type the left hand side into your calculator (make sure it's in degree mode) and you've solved the equation.

#### Attached Whiteboard:

4 years ago This is "isosceles right triangle"

The opposite and adjacent sides are equal

c = 17cm

c2 = a2 + a2  $\rightarrow$ c2 = 2a2

a2 = c2 $\div$÷ 2

= $\frac{17^2}{2}$1722

=144.5

a = $\sqrt{144.5}$144.5

=12.02cm