# Thread: problem solving with triangles.

1. ## problem solving with triangles.(only 2 more questions)

2)If a car drives 100km North and then 45km East, determine the distance and the direction that you will be from your departure position.

3)If I head across a river paddling my canoe at 6km/h N, but the river current is moving at 3km/h E, determine the speed and direction of my canoe relative to the shore.

answer any of these 2 you know you dont have to answer them all.

2. 1)If a 9.3 meter tree casts a shadow that is 12.4m, determine the angle of elevation of the sun.

The bottom of the tree, the top of the tree, and the tip of the shadow will give you a nice right triangle. We want the angle of elevation, $\displaystyle \theta$. Recall SOH-CAH-TOA: sin is opposite over hypotenuse; cos is adjacent over hypotenuse; tan is opposite over adjacent. We know the height of the tree and the length of the shadow. Let's use this knowledge. The height of the tree is the side opposite the angle of elevation. Thus, we have 9.3 meters as our side opposite the angle of elevation. The length of the shadow is the side adjacent (and not the hypotenuse) to the angle of elevation. Thus, we have 12.4 meters as our side adjacent to the angle of elevation. Given that we have the opposite and adjacent side lengths, we will be using tangent to get our answer. Namely, we will need to compute the inverse tangent of the height of the tree over (divided by) the length of the shadow.

$\displaystyle \theta = \tan^{-1} (\frac{9.3}{12.4}$)

Finish this! (using a calculator)

-Andy

3. Hi,

here the height of the tree=9.3m