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15 Cards in this Set
- Front
- Back
Are these two triangles similar? If so, explain how you know and write a similarity statement.
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The two triangles are similar by the AA similarity theorem, which states that two triangles are similar if and only if two angles of one triangle are congruent to two angles of the other triangle. Since,
m∠E=m∠P=33° and m∠F=m∠Q=45°, ∠E≈∠P and ∠F≈∠Q. Therefore, ∆EFG~∆PQR. |
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Given ∆NOP ~ ∆HIJ, find the missing side length.
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Because the triangles are similar, the side lengths are proportional, so,
OP/HJ=NO/HI x/12=1/6 x=12(1)/6 x=12/6=2. The missing side length is 2cm. |
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Are these two triangles similar? If so, explain how you know and write a similarity statement.
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The angles of a triangle add to 180⁰.
Since m∠S+m∠T=79+64=143, m∠R=37. Since m∠M+m∠N=79+60=139, m∠L=41.m∠S=m∠M=79° but m∠T ≠ m∠N or m∠L |
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You're flying a kite that is 200 feet high. The kite string makes a 50d angle from the ground (M). Find the length of the kite string to the nearest foot using a trig ratio.
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The sine ratio for any acute angle θ of a right triangle is as follows:
sinθ= opposite/adjacent sin50°= 200/x sin50°(x)= 200 0.776x=200 x=200/0.776 x=257.73 ft |
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A tree that is 70 feet tall casts a shadow that is 35 feet long. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground? Use a trig ratio to find the angle.
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The tangent ratio for any acute angle θ of a right triangle is as follows:
tan θ= opposite/adjacent tan V= 70/35 tan V= 2 tan⁻¹ (2)= 63.43° |
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A bird sits on top of a tree. The angle of depression from the bird to the feet of an observer standing 25 meters away from the tree is 35°. What is the height of the tree? Use a trig ratio to find the height.
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The tangent ratio for any acute angle θ of a right triangle is as follows:
tanθ = opposite/ adjacent tan35⁰ = x/25 25tan35⁰= x 25(.700) = x x = 17.5 m |
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Jacob lives in an apartment. He comes to his apartment from the school. He saw that his building casts a shadow that is 45 m long. He then sees the top of the buidling. The slope of the building is 65 m long. What is the height of the building?
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We know that a²+b²=c² where a and b are the legs and c is the hypotenuse.
Therefore, (45)²+b²=(65)² 2025+b²=4225 b²=2200 b=√2200 b=46.9 meters |
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One day Earl went to the garden. He was playing around the tree. He stays at point A, where the shadow of the tree ends. The distance from that point, to the top of the tree (point C) is 75 ft. The measured height of the tree is 55 ft. How far away from the tree is Earl?
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We know that a²+b²=c² where a and b are the legs and c is the hypotenuse. Therefore, (55)²+b²=(75)²
3025+b²=5625 b²=2600 b=√2600 b=50.99 feet |
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Irvin is a little boy; he loves shining star stickers. His mother pastes a shining star sticker at the point R, which is the top of the cupboard. The height of the cupboard is 20 ft. Irvin looks from his knees at the point Q and saw the sticker. His position makes a 25° angle. What is the distance from point Q to point R?
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The sine ratio for any acute angle θ of a right triangle is as follows:
sinθ=opposite/hypotenuse sin25°=20/x sin25⁰(x)=20 0.4226x=20 x=47.33 ft |
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Katie is flying a kite. The string of the kite makes an angle of 20° from the ground. If the height of the kite is 20 m, find the length in meters of the string that Katie is using.
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sinθ=opposite/hypotenuse
sinθ=ON/NM sin(20⁰)= 20/x sin(20⁰)(x)=20 0.3420x=20 x=20/0.3420 x=50.48 m |
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Two trees face each other separated by a distance of 40 m. As seen from the top of the second tree, the angle of depression to the first tree's base is 50°. Find the height of the second tree in meters.
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tanθ= opposite/adjacent
tanθ= AB/BC tan(50⁰)=x/40 40tan(50⁰)=x 40(1.191)=x x=47.64 m |
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A 15 inch long ladder is leaning against a wall, at the point X. Point Y is the bottom of the ladder, which makes a 32° angle with the ground. Find the distance of a wall from the bottom of the ladder.
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cosθ= adjacent/hypotenuse
cos(32⁰)=YZ/YX cos(32⁰)=x/15 15cos(32⁰)=x 15(.848)=x 12.72 in=x |
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A tree is 50 ft in height and casts a shadow that is 25 feet long. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground? (Assuming that the tree is 100% straight)
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tanθ=opposite/adjacent
tan(x)=50 ft/25 ft tan(x)=2 ft tan⁻¹(2)=63.43° |
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Bob is building a new home. He needs to erect a wall that previously was not in the plans. A square section of the housing wall requires diagonal bracing. If the wall is 6.5 meters, how long must the brace be?
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We know that a²+b²=c² where a and b are the legs and c is the hypotenuse. Therefore,
(6.5)²+(6.5)²=c² 42.25+42.25=c² 84.5=c² c=√84.5 c=9.19 m |
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What is the relationship between the sine and cosine of complementary angles?
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Sin(A)=cos(90-A)
Cos(A)=sin(90-A) |
