Trigo - solving triangles

Question 1

Find angle ACB correct to 1 decimal place

Answer 1

cos ACB = 6/10

ACB = cos^-1(6/10)

= 53.1º

Question 2

Find the length AB correct to 3 significant figures

Answer 2

AB² = 10² - 6²

^{= 64}

^{AB = sqrt (64)}

^{= 8.00 cm}

Question 3

Find angle QPR correct to 1 decimal place

Answer 3

sin QPR = 5/13

ACB = sin^-1(5/13)

= 22.6º

Question 4

Find the length PR correct to 3 significant figures

Answer 4

PR² = 13² - 5²

^{= 144}

^{PR = sqrt (144)}

^{= 12.0 cm}

Question 5

Find angle TUV correct to 1 decimal place

Answer 5

tan TUV = 7/24

TUV = tan^-1(7/24)

= 16.3º

Question 6

Find the length UT correct to 3 significant figures

Answer 6

UT² = 24² + 7²

^{= 625}

^{UT = sqrt (625)}

^{= 25.0 cm}

Question 7

Find the value of x correct to 3 significant figures

Answer 7

cos 33 = x/21

x = 21 * cos 33

= 17.6