Sam is trying to build a house on a vacant plot, but there is a tree in his way. He wants to determine the height of the tree before he cuts it down to make sure he can fit the rest of the tree in a flatbed truck to move it off of the land. Sam does not have a way of measuring the tree directly, so he will need to measure it using trigonometry
Sam knows his kneeling height is 4'3", and determines that his eye line inclines 64.2 degrees to view the top of the tree, and Sam knows he is kneeling 5' away from the tree base. Using this information he can determine the height of the tree using tangent ratios. Sam first determines the tangent of 64.2, then multiplies it by 5 with the final answer of 10.34 ft
Now Sam needs to know how far to move the Bulldozer backwards to catch the falling tree to make loading it into the truck easier. Sam knows that the arm is raised 2' and the angle of the "blade" is 35 degrees towards the ground. Using sin, he determines that 2 divided by the sin of 35 will give him the answer to how the tree will land on the "blade".
With the answer of 3.5', Sam determines that the point of impact will be 3.5' from the base of the tree, landing on the Bulldozer's arm, effectively catching it.
As Sam waits for his shipment of bricks to arrive, he gets bored and decides to measure the angle at which the ladder he is using has. He knows that the ladder stands 6' tall and the actual ladder part is 7.5'. Using trigonometry, he is able to determine the cosine of the angle by dividing 6 by 7.5, giving him the cosine of the ladder's angle.
Once the cosine had been found, Sam punched in the cosine value and use the arc cosine to determine the angle, which was 36.9 degrees.