Right Angled Trig

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#13794

Right Angled Trig

SOH CAH TOA

$$\sin\theta=\frac{opp}{hyp}$$	$$\cos\theta=\frac{adj}{hyp}$$	$$\tan\theta=\frac{opp}{adj}$$
$$c^2=a^2+b^2$$

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#18715

ABCD is a rectangle. AC = 15 cm and AD = 13 cm. Find ∠ACD, correct to the nearest degree.

$$\sin\;\angle ACD =\frac{13}{15}$$
∠ACD = 60º
remembering that when you name the rectangle, to go in one direction only

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#18716

Lucy wants to clean out the gutter on her house. The gutter is 9.3 m above the ground. Lucy knows that a ladder must extend at least 80 cm beyond a gutter to be safe. If the ladder makes an angle of 70° with the ground, determine the shortest ladder ( to the nearest cm) that is safe for Lucy to use.
	Draw a triangle with the information provided we have opp = 9.3 and hyp = x, so we use sin to find x
$$\sin 70^{\circ}=\frac{9.3}{x}$$	since x is the denominator we divide
$$x=\frac{9.3}{\sin 70^{\circ}}$$	remember, the number always goes first and the trig will be on the bottom
x = 9.8968m	calculate
x = 9.90m	rounding that to the nearest cm, which is 2 decimal places, as there are 100 cm in a m
Length = 9.90 + 0.8 = 10.70 m	since we need an extra 80cm, then we add 0.8m to our answer

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#18717

A 3 m ladder just reaches a window 2 m above the floor. What angle does the ladder make to the floor?
	Draw a diagram showing all the information given and mark the angle the 3m ladder will form the hypotenuse, and the 2m up the wall is opposite the angle we want, which is between the ladder and the ground
##\sin x=\frac{2}{3}##	as we have opposite and the hypotenuse, use the sin ratio
x = 42°	because we are looking for an angle, we shift sin the 2 over 3

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#18719

For the triangle shown, find sin θ is:
c2 = 122 + 26.22 c2 = 830 c = 28.8	Because we want sin, we are going to need the hypotenuse, so we use Pythagoras to obtain the hypotenuse: a2 + b2 = c2
$$\sin\theta=\frac{12}{28.8}$$	12 is opposite $$\theta$$ 28.8 is the hypotenuse
$$\sin\theta=\frac{12}{28.8}$$	calculate
$$\sin\theta=0.417$$	we are not being asked to find $$\theta$$, so we just calculate the ratio – do not shift sin

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