Geometry Triangle assignment

  1. Find the measures of the following to the nearest tenth of a degree.
geometry triangle assignment image 1

Solution

  1. HT is the hypotenuse of a right angled triangle HWT thus we use Pythagoras theorem stating a2 + b2 = c2 where c is the hypotenuse side thus Ht2 = hw2 +wt2

Ht2 =152 + 82, HT2 = 289, HT= √ (289), HT =17

  1. 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

  1. What is the area of the given triangle?
geometry triangle assignment image 2

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 cm2

  1. If X and Y are complementary angles sinX=15/17, and cosX=8/17, find each of the following :
  1. tan X =
  1. sin Y =
  1. cos Y =
  1. 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 82 = 152 =172=289

geometry triangle assignment image 3
  1. Tan x =opposite/ adjacent = 15/8 =1.875
  2. Sin y = opposite/hypotenuse = 8/17 = 0.4706
  3. Cos y= adjacent/ hypotenuse = 15/17 = 0.8824
  4. Tan y = opposite/hypotenuse =8/15 = 0.5333
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