Tutor profile: Surya R.

A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees. Estimate the height h of the tree to the nearest tenth of a meter.

This problem will need some illustration as solving problems like these are much easier with diagrams. /| / | / | h / | / 18___ | x 100 given the tools that we have, this is the best diagram that we can create. In order to find h, we have to use trigonometry ratios. The trig ratios are Sin, Cosine, Tan. You have to have some background knowledge, but for the sake of this example, we will be using tan. The ratio for tan is tan(degree) = opposite / adjacent --> tan(18) = h/100, now we have to solve for h --> we have to put this in the calculator and we get 32.5 meters.

What is the sum of interior angles in a Hexagon?

For this problem, we need to know what the formula for interior angles is. It is --> (number of sides - 2) * 180 Now that we know the formula we have to plug in the information we know. How many sides does a hexagon have? 6 sides! --> (6-2) * 180 --> 4*180 --> 720 the sum of interior angles in a hexagon is 720 degrees.

The length of a rectangle is twice that of the width. The perimeter of the rectangle is 24 cm. What is the width of the rectangle? Length?

The information we need to know for this question is the formula for perimeter of a rectangle. the rectangle perimeter formula is: width + width + length + length --> (2w + 2L) = perimeter given the information given, we can have to write an expression that shows the length in terms of the width. Since the length is twice the width we can say that L = 2W. Width is denoted as W. Using the formula we have above we just need to plug in the information we know. We know that width is just W and length is 2W --> 2(w) + 2(2w) = 24 --> combine like terms --> 6w = 24 --> w = 24/6 --> w = 4 Width is 4 Length is L = 2W --> L = 2(4) --> L = 8