# Geometry Triangle Assignment

- Find the measures of the following to the nearest tenth of a degree.

**Solution**

- HT is the hypotenuse of a right angled triangle HWT thus we use Pythagoras theorem stating a
^{2}+ b^{2}= c^{2 }where c is the hypotenuse side thus Ht^{2}= hw^{2}+wt^{2}

Ht^{2} =15^{2} + 8^{2}, HT^{2} = 289, HT= √ (289), HT =17

- Angle T we use cosine where cosine of angle T is adjacent side to this angle t divided by hypotenuse. Thus cos inverse of this value gives us value of <T

COS (T) = 8/17, <T = COS^{-1 }(8/17), <T cos-1(0.4706) = 61.9 ^{0}

<T = 61.9 ^{0}

- What is the area of the given triangle?

**Solution **

To calculate the area of the above triangle we will use the formula,

Area = ½ *a*b * sin (c) ,where a and b are any two given sides of the triangle and c is the angle between the two sides thus

Area = ½ *7*13* sin (38), 1/2*7cm*13cm*sin (38) = 28.0126 cm^{2}

- If X and Y are complementary angles sinX=15/17, and cosX=8/17, find each of the following :

- tan X =

- sin Y =

- cos Y =

- tsn Y =

**Solution**

First we put the given information into a diagram

We know Sin x = opposite side /hypotenuse side, cos x = adjacent side /hypotenuse

Thus this is a triangle with opposite side =15, adjacent side = 8 and hypotenuse =17

Also it’s a right angled triangle since 8^{2} = 15^{2} =17^{2}=289

- Tan x =opposite/ adjacent = 15/8 =1.875
- Sin y = opposite/hypotenuse = 8/17 = 0.4706
- Cos y= adjacent/ hypotenuse = 15/17 = 0.8824
- Tan y = opposite/hypotenuse =8/15 = 0.5333

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