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kiruha [24]
2 years ago
7

2C%20AB%20%3D%208%20%5C%3A%20%20cm%20%20%5C%3A%20and%20%5C%3A%20%20BC%20%3D%206%20%20%5C%3A%20cm.%20Find%20%5C%3A%20%20the%20%5C%3A%20%20length%20%5C%3A%20%20of%20%5C%3A%20%20AC.%20%7D%7D" id="TexFormula1" title="\color{red}{\tt {In \: Δ \: ABC, ∠B=90, AB = 8 \: cm \: and \: BC = 6 \: cm. Find \: the \: length \: of \: AC. }}" alt="\color{red}{\tt {In \: Δ \: ABC, ∠B=90, AB = 8 \: cm \: and \: BC = 6 \: cm. Find \: the \: length \: of \: AC. }}" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
Sliva [168]2 years ago
6 0

Answer:

Solution given;

<B=90

so

AB=b=8cm

BC=p=6cm

AC=h=?

by using Pythagoras law

h²=p²+b²

h=√{6²+8²)

h=10cm

so

<u>length</u><u> </u><u>of</u><u> </u><u>AC</u><u>=</u><u>1</u><u>0</u><u>c</u><u>m</u><u>.</u>

makkiz [27]2 years ago
5 0

Use Pythagoras theorem

Hypotenuse²=Base²+ Height ²

H²=(8)²+(6)²

H²=64+36

H²= 910

H²=10√91 cm Solution

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7 0
2 years ago
Fred the owl is looking down at a 67° angle from the top of a tree that is 15 ft tall, when he spots a bird on the ground. How f
guapka [62]

Answer:

Fred     C. 16.30 ft

Gary     B. 169.67 m

Step-by-step explanation:

Fred the owl...

Always <u>draw a diagram first</u> (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.

We need to <u>find "x"</u>, which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.

∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.

<u>Use the trig. ratio sine</u> because it has opposite and hypotenuse in it. The general formula is:

sinθ = opp/hyp

θ means the angle, and we know it is 67°.

Replace all the information you know:

sinB = opp/hyp

sin67° = (15ft) / x     Isolate "x". Rearrange the equation.

xsin67° = (15ft)         Divide both sides by sin67°

x = (15ft) / sin67°

x = 16.295... ft   Exact answer in decimals

x ≈ 16.30 ft     Rounded to nearest hundredth

Therefore Fred the owl is 16.30 feet from the bird.

Gary spots a monkey...

Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to <u>find "x"</u>, which is the distance between the monkey and the bottom of the tower.

The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. <u>The trig. ratio that has adjacent and opposite is tangent.</u>

tanθ = opp/adj

Replace all the information you know:

tanM = opp/adj

tan69° = (442m) / x    Rearrange the formula to isolate "x"

xtan69° = 442m         Divide both sides by tan69°

x = 442m / tan69°      Solve by dividing

x = 169.6679.... m    Exact decimal answer

x ≈ 169.67m            Rounded to the nearest hundredth

Therefore the monkey is 169.67 metres from the tower.

Remember all the trig. ratios using the acronym SohCahToa.

o = opposite side

a = adjacent side

h = hypotenuse side

S = sine, sin for short

C = cosine, cos for short

T = tangent, tan for short

The operation is always dividing the first side in the acronym by the second side.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

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maksim [4K]
19/100 would be 19%.
Here ya go

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