trigonometry

1. solve for h or $\theta$
a)
image of right triangle with hypotenuse 28, angle $38^\circ$, and opposite side h
b)
image of right triangle with hypotenuse 52, adjacent side 38, and angle $\theta$
c)
image of right triangle with hypotenuse 125, angle $35^\circ$, and adjacent side h
d)
image of right triangle with opposite side 21.6, angle $46^\circ$, and adjacent side h
e)
image of right triangle with hypotenuse 64, opposite side 18, and angle $\theta$
f)
image of right triangle with hypotenuse 124, angle $30^\circ$, and adjacent side h
g)
image of right triangle with opposite side 4.8, adjacent side 12.9, and angle $\theta$
h)
image of right triangle with opposite side 16.2, adjacent side 35.9, and angle $\theta$
i)
image of right triangle with opposite side 23, adjacent side 18, and angle $\theta$
j)
image of right triangle with hypotenuse 24, angle $18^\circ$, and opposite side h

2. a tree casts a shadow that is 15 yd. long when the angle between the suns rays and the ground is $37^\circ$. what is the height of the tree to the nearest foot?

3. in this trapezoid, determine the measure of $\angle w$ to the nearest tenth of a degree.
image of trapezoid wxyz with sides wz = 19 cm, wx = 23 cm, xy = 6 cm

4. a. determine the perimeter of $\delta abc$ to the nearest tenth of an inch.
image of triangle abc with angle b = $38^\circ$, side bc = 4.5 in
b. determine the area of $\delta abc$ to the nearest square inch.

5. a tree is supported by four guy wires. all the guy wires are anchored to the ground at points 3 m from the base of the tree. the guy wires are attached to the tree at a height of 4.5 m above the ground. to the nearest tenth of a degree, determine the measure of the angle of inclination of a guy wire.

Question

trigonometry

1. solve for h or $\theta$
a)
image of right triangle with hypotenuse 28, angle $38^\circ$, and opposite side h
b)
image of right triangle with hypotenuse 52, adjacent side 38, and angle $\theta$
c)
image of right triangle with hypotenuse 125, angle $35^\circ$, and adjacent side h
d)
image of right triangle with opposite side 21.6, angle $46^\circ$, and adjacent side h
e)
image of right triangle with hypotenuse 64, opposite side 18, and angle $\theta$
f)
image of right triangle with hypotenuse 124, angle $30^\circ$, and adjacent side h
g)
image of right triangle with opposite side 4.8, adjacent side 12.9, and angle $\theta$
h)
image of right triangle with opposite side 16.2, adjacent side 35.9, and angle $\theta$
i)
image of right triangle with opposite side 23, adjacent side 18, and angle $\theta$
j)
image of right triangle with hypotenuse 24, angle $18^\circ$, and opposite side h

2. a tree casts a shadow that is 15 yd. long when the angle between the suns rays and the ground is $37^\circ$. what is the height of the tree to the nearest foot?

3. in this trapezoid, determine the measure of $\angle w$ to the nearest tenth of a degree.
image of trapezoid wxyz with sides wz = 19 cm, wx = 23 cm, xy = 6 cm

4. a. determine the perimeter of $\delta abc$ to the nearest tenth of an inch.
image of triangle abc with angle b = $38^\circ$, side bc = 4.5 in
b. determine the area of $\delta abc$ to the nearest square inch.

5. a tree is supported by four guy wires. all the guy wires are anchored to the ground at points 3 m from the base of the tree. the guy wires are attached to the tree at a height of 4.5 m above the ground. to the nearest tenth of a degree, determine the measure of the angle of inclination of a guy wire.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ], "current_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ] } ## Identify given values and trigonometric relationship $$ \begin{aligned} &\text{Shadow length (adjacent side): } d = 15\text{ yd} = 45\text{ ft}\ &\text{Angle of elevation: } \theta = 37^\circ\ &\text{Height of the tree (opposite side): } h\ &\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{d} \end{aligned} $$ ## Calculate the height in feet $$ \begin{aligned} &h = 45 \cdot \tan(37^\circ)\ &\tan(37^\circ) \approx 0.75355\ &h \approx 45 \cdot 0.75355 \approx 33.91\text{ ft} \end{aligned} $$ ## Round to the nearest foot $$ h \approx 34\text{ ft} $$ $34\text{ feet}$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given values and trigonometric relationship

Calculate the height in feet

Round to the nearest foot

Answer: