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3 years ago

What is the base of a triangle with a height of 14 cm and an area of 42 square cm?

Mathematics

2 answers:

sasho [114]3 years ago

5 0

Answer:

$6cm$

Step-by-step explanation:

$area = \frac{1}{2} \times base \times height \\ 42 = \frac{1}{2} \times b \times 14 \\ 42 = \frac{14b}{2} \\ 42 = 7b \\ \frac{42}{7} = \frac{7b}{7} \\ base = 6cm$

hope this helps

Naily [24]3 years ago

4 0

Answer:

Step-by-step explanation:

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1. A MAP SCALE READS 1CM:5KM. IF A DISTANCE ON THE MAP MEASURES 7CM, THE ACTUAL DISTANCE WILL BE?. 2. A SCHOOL DINING HALL IS 35

Agata [3.3K]

Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. $42^\circ$

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map = 7 cm

Actual distance = Measurement of map $\times 5$

Actual distance = 7 $\times 5$ = 35 km

-------------------

Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

-------------------

Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to $\frac{1}{5}$ cm on scale

30m is equivalent to $\frac{1}{5} \times 30$ = 6 cm on scale

-------------------

Solution 4.

Angle of elevation of A from B = $42^\circ$

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = $42^\circ$

-------------------

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, $\angle B = 42^\circ$

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

$sin\theta = \dfrac{Perpendicular}{Hypotenuse}$

$sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m$

============

So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. $42^\circ$

5. 16.73 m

7 0

3 years ago