In the sketch alongside, DF is a vertical flagpole and $$ \mathrm{E}, \mathrm{F} $$ and G are three points on ground level. $$ \mathrm{DF}=7 \mathrm{~m}, \mathrm{EF}=6 \mathrm{~m}, \mathrm{FDG}=38^{\circ} $$ and $$ \mathrm{FEG}=42^{\circ} $$. $$ \mathrm{EGF}= heta $$, where $$ heta $$ is an acute angle. Calculate (1) the magnitude of $$ heta $$. (2) the length of EG (3) the magnitude of EDG. (4) the area of $$ riangle \mathrm{EDG} $$. (5) the angle of elevation of D from E .

Question

In the sketch alongside, DF is a vertical flagpole and $$ \mathrm{E}, \mathrm{F} $$ and G are three points on ground level. $$ \mathrm{DF}=7 \mathrm{~m}, \mathrm{EF}=6 \mathrm{~m}, \mathrm{FDG}=38^{\circ} $$ and $$ \mathrm{FEG}=42^{\circ} $$. $$ \mathrm{EGF}=	heta $$, where $$ 	heta $$ is an acute angle. Calculate (1) the magnitude of $$ 	heta $$. (2) the length of EG (3) the magnitude of EDG. (4) the area of $$ 	riangle \mathrm{EDG} $$. (5) the angle of elevation of D from E .

UpStudy AI · Accepted Answer

To solve this problem, we will use trigonometry and the properties of triangles.

Given:
- $$ \mathrm{DF} = 7 \, 	ext{m} $$
- $$ \mathrm{EF} = 6 \, 	ext{m} $$
- $$ \mathrm{FDG} = 38^\circ $$
- $$ \mathrm{FEG} = 42^\circ $$
- $$ \mathrm{EGF} = 	heta $$ (acute angle)

We need to calculate:
1. The magnitude of $$ 	heta $$
2. The length of EG
3. The magnitude of EDG
4. The area of $$ 	riangle \mathrm{EDG} $$
5. The angle of elevation of D from E

Let's start by calculating the magnitude of $$ 	heta $$ using the given angles.
Calculate the value by following steps:
- step0: Calculate:
  $$38+42$$
- step1: Add the numbers:
  $$80$$
The magnitude of $$ 	heta $$ is $$ 80^\circ $$.

Next, we will calculate the length of EG.
Calculate the value by following steps:
- step0: Calculate:
  $$6	an\left(80ight)$$
The length of EG is approximately 54.02193 m.

Now, we will calculate the magnitude of EDG.
Calculate the value by following steps:
- step0: Calculate:
  $$7	an\left(80ight)$$
The magnitude of EDG is approximately 63.025585 m.

Next, we will calculate the area of $$ 	riangle \mathrm{EDG} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}	imes 6	imes 63.025585$$
- step1: Multiply the terms:
  $$3	imes 63.025585$$
- step2: Multiply the numbers:
  $$189.076755$$
The area of $$ 	riangle \mathrm{EDG} $$ is approximately 189.076755 m².

Finally, we will calculate the angle of elevation of D from E.
Calculate the value by following steps:
- step0: Calculate:
  $$\arctan\left(\frac{7}{6}ight)$$
The angle of elevation of D from E is approximately 0.86217 radians or 49.3°.
1. $$ 	heta = 80^\circ $$ 2. $$ EG \approx 54.02 \, 	ext{m} $$ 3. $$ EDG \approx 63.03 \, 	ext{m} $$ 4. Area of $$ 	riangle \mathrm{EDG} \approx 189.08 \, 	ext{m}² $$ 5. Angle of elevation of D from E is approximately $$ 49.3^\circ $$

In the sketch alongside, DF is a vertical flagpole and
and G are three points on ground level.
and .
, where is an acute angle.
Calculate
(1) the magnitude of .
(2) the length of EG
(3) the magnitude of EDG.
(4) the area of .
(5) the angle of elevation of D from E .

Upstudy AI Solution

Answer

Solution

Beyond the Answer

1. Calculate the magnitude of

2. Calculate the length of

3. Calculate the magnitude of

4. Calculate the area of

5. Calculate the angle of elevation of from

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In the sketch alongside, DF is a vertical flagpole and and G are three points on ground level. and . , where is an acute angle. Calculate (1) the magnitude of . (2) the length of EG (3) the magnitude of EDG. (4) the area of . (5) the angle of elevation of D from E .