This week in Math, I learned how to find the measure of an angle of a right triangle with two side lengths. First you need to need to label the triangle sides relative to the angle you are trying to find. The hypotenuse is the longest side. The adjacent is the side next to the angle that isn’t the hypotenuse. The opposite is the side opposite of the angle. Next, with the two side lengths you are given, you need to find the trigonometric function that works with the side lengths you are given. sin=opposite/hypotenuse, cos=adjacent/hypotenuse, and tan=opposite/adjacent.

As you can see in this example, we are given the side lengths of opposite and adjacent, therefore, we use tan=opposite/adjacent. We know that in this example, opposite=9.7 and adjacent=5.2. So in our calculator we would type in then press “=”. The answer we get should be something like 61.80502… which would round to 62, so our answer would be , and that is how you find the measure of an angle of a right triangle with only two side lengths.

This week in Math, I learned how to calculate the surface area of a sphere. All you have to do is insert the measurements into this formula: 4πr^2 and you will find your answer. In this formula, you will need either the radius or the diameter which you can then turn to radius.

The radius is the distance between the centre of the circle to the outer edge and is represented by “r” in the diagram above. If you are given the diameter, represented by “d” above, all you need to do is divide that number by 2 and take that number.

Let’s say for example that the radius(r) of the circle above was 2. All you would need to do is plug that number into the formula(4πr^2) to figure out your answer like this on your calculator:

This week I learned how to read measurements on a micrometer.

First you have to put your object into your micrometer then twist the thimble it until the object is tight inside. Then, you would read the last visible number on the sleeve/barrel which will tell you how many millimeters to start with by 0.5mm increments. Then, you would look at the number on the thimble that matches up with the centre line and divide that number by a hundred then add that to your initial measurement on the barrel.

In this example, you can see that the last visible number on the barrel is 16.5. You can also see that the number on the thimble reads 16. With that you add 0.16 to 16.5 which equals 16.66, so the measurement of your object is 16.66mm.

This week I learned that you can turn numbers with fractional exponents into a radical. The numerator of the fraction would be the power of the radical and the denominator would be the index of the radical.

In this example, the “2” would become the power of the radical, and the “3” would become the index of the radical like this: