Tutor profile: Ninna R.
Given an angle of $$30°$$, what is the length of the opposite side of a right triangle whose hypotenuse is $$5$$ meters?
The function tangent $$tanθ$$ is the ratio of $$Opposite/ Hypotenuse$$ or $$tanθ = O/ H$$ With the given angle of $$30°$$ and a hypotenuse side of $$5$$, we have $$tan(30°) = O/ 5$$ Using the calculator, we determine $$tan(30°)$$ to be $$0.577... $$ $$0.577... $$ is the ratio of the lengths of the triangle which means that the opposite side is around $$0.577... $$ times as long as the hypotenuse. We then place this value for $$tan(30°)$$, giving us $$0.557... = O/5$$ By multiplying the value of hypotenuse with the $$0.577... $$ we get $$(0.557...)(5) = O$$ $$2.886...=O$$ By rounding off to two decimal places, the opposite side of the right triangle is $$2.89$$ meters.
What is the hypotenuse of a right triangle whose sides are 4 and 3?
Using the Pythagorean Theorem, we calculate the hypotenuse (or the longest side of the triangle) by adding the squares of the lengths or sides of the right triangle. In other words, let's say that $$a$$ and $$b$$ are the sides while $$c$$ is the longest side or the hypotenuse, we therefore have $$a^2 +b^2 = c^2$$. The Pythagorean Theorem can be use to calculate the length of the hypotenuse of right triangle if two sides are known. Knowing these, we can determine the hypotenuse through $$√(a^2 +b^2) = c$$. So if $$a=4$$ and $$b=3$$, then we have $$4^2 +3^2 = c^2$$. $$√(4^2 +3^2) = c$$. $$√25 = c$$ $$5 = c$$ So the hypotenuse of a right triangle whose sides are 4 and 3 is 5.
Simplify this expression: $$-7X + 3Y + 12X - 9Y$$
We simplify an algebraic expression by combining like terms. Terms having the same variable are considered as "like terms". In our given expression, $$-7X$$ and $$12X$$ have the same variable of $$X$$ and therefore are like terms. $$3Y$$ and $$-9Y$$ are like terms too for they have the same variable $$Y$$. The cool part about this is you can combine them together by adding their coefficients, and forming a single term! So, in our given expression, we combine $$-7X$$ and $$12X$$: $$=(-7 + 12)X$$ $$= 5X$$ And we combine $$3Y$$ and $$-9Y$$: $$=(3 - 9)Y$$ $$= -6Y $$ So the simplified expression therefore is $$5X - 6Y$$