(i) Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places. (ii) Write 3° 14' in DMS (i.e. degrees, minutes, and seconds). (b) The diagram shows a right-angled triangle, with the angle A marked. Given that cos A = sin A, show that this triangle must be isosceles. (c) A right-angled triangle has sides of length 7 cm, 24 cm, and 25 cm. Find the size of the smallest angle in this triangle. Give your answer correct to one decimal place.

Junior Cycle Mathematics Trigonometry: (i) Write 2° 43' 5'' in degrees

(i) Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places - Junior Cycle Mathematics - Question 8 - 2016

Question 8

(i) Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places. (ii) Write 3° 14' in DMS (i.e. degrees, minutes, and seconds). (b) The diagram show... show full transcript

Worked Solution & Example Answer:(i) Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places - Junior Cycle Mathematics - Question 8 - 2016

Step 1

Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places.

96%

114 rated

Answer

To convert from degrees, minutes, and seconds to decimal degrees, we can use the formula:

ext{Decimal Degrees} = ext{Degrees} + \frac{ ext{Minutes}}{60} + \frac{ ext{Seconds}}{3600}

Here, we have:

Degrees = 2
Minutes = 43
Seconds = 5

Substituting these values, we get:

ext{Decimal Degrees} = 2 + \frac{43}{60} + \frac{5}{3600} = 2 + 0.7167 + 0.0014 = 2.7181

Rounding to two decimal places gives us:

Answer: 2.72°

Step 2

Write 3° 14' in DMS (i.e. degrees, minutes, and seconds).

99%

104 rated

Answer

To convert from decimal degrees to DMS:

Degrees = 3
Decimal Part = 0.14

Now convert the decimal part to minutes:

Minutes = 0.14 × 60 = 8.4 minutes

Since 0.4 minutes is 24 seconds (0.4 × 60), we have:

So, 3° 14' becomes: 3° 8' 24''

Answer: 3° 8' 24''

Step 3

Given that cos A = sin A, show that this triangle must be isosceles.

96%

101 rated

Answer

Since we have:

\cos A = \sin A

Using the definitions of cosine and sine:

\frac{\text{adjacent}}{\text{hypotenuse}} = \frac{\text{opposite}}{\text{hypotenuse}}

Cross-multiplying gives us:

\text{adjacent} = \text{opposite}

This means that the two non-hypotenuse sides of the triangle are equal, indicating that the triangle is isosceles.

Conclusion: Triangle is isosceles.

Step 4

Find the size of the smallest angle in this triangle.

98%

120 rated

Answer

To find the smallest angle in the triangle with sides 7 cm, 24 cm, and 25 cm, we can use the sine rule:

\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{25}

Calculating this gives:

A = \sin^{-1}\left(\frac{7}{25}\right) \approx 16.36°

Rounding to one decimal place:

Answer: 16.4°

(i) Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places - Junior Cycle Mathematics - Question 8 - 2016

Worked Solution & Example Answer:(i) Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places - Junior Cycle Mathematics - Question 8 - 2016

Write 2° 43' 5'' in degrees in decimal form, correct to two decimal places.

Write 3° 14' in DMS (i.e. degrees, minutes, and seconds).

Given that cos A = sin A, show that this triangle must be isosceles.

Find the size of the smallest angle in this triangle.

Join the Junior Cycle students using SimpleStudy...