Question
The diagram shows a right-angled triangle.
Calculate $AB.$
▶️Answer/Explanation
$6.39$
the cosine rule
$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$
$\cos(37^\circ) = \frac{AB}{8}$
$AB = 8 \times \cos(37^\circ)$
$\cos(37^\circ) \approx 0.7986$
$AB = 8 \times 0.7986$
$AB \approx 6.39 \, \mathrm{cm}$
Question
The diagram shows a flagpole, $BD$, held by two ropes, $AD$ and $CD$.
$ABC$ is a straight line and angle $\angle ABD = 90^\circ$.
\(AD = 21.2 \, \text{m}, \, AB = 16.5 \, \text{m}, \, \text{and angle } \angle BCD = 48^\circ.\)
(a) Show that the height of the flagpole $BD$ is $13.3 \, \text{m}$, correct to 1 decimal place.
(b) Calculate the length of the rope $CD$.
▶️Answer/Explanation
$(\mathbf{a})~ [BD= ] \sqrt {21. 2^2- 16. 5^2}$
$13.31\ldots$
$(b)$ $17.9$ or $17.89$ to $17.91$
(a)
Pythagoras’ Theorem
$AD^2 = AB^2 + BD^2$
$(21.2)^2 = (16.5)^2 + BD^2$
$449.44 = 272.25 + BD^2$
$BD^2 = 449.44 – 272.25$
$BD^2 = 177.19$
$BD = \sqrt{177.19} \approx 13.31 \, \text{m}$
(b)
$\sin(48^\circ) = \frac{BD}{CD}$
$\sin(48^\circ) = \frac{13.3}{CD}$
$0.7431 = \frac{13.3}{CD}$
$CD = \frac{13.3}{0.7431}$
$CD \approx 17.9 \, \text{m}$
Question
The diagram shows a right-angled triangle.
Calculate the value of x.
▶️Answer/Explanation
$52.6$ or $52.61$ to $52.62$
$
\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}
$
$
\cos(x) = \frac{8.5}{14}
$
$
\cos(x) = 0.6071
$
$
x = \cos^{-1}(0.6071)
$
$
x \approx 52.6^\circ
$
Question
(a) Calculate AD.
(b) Use trigonometry to calculate angle BCD.
Answer/Explanation
(a)3.54
(b)44.3
Question
Calculate the value of x.
Answer/Explanation
Ans: 23.2
Question
The diagram shows a ladder of length 8m leaning against a vertical wall.
Use trigonometry to calculate h.
Give your answer correct to 2 significant figures.
Answer/Explanation
Ans:
h = 6.6 cao
Question
Calculate AB.
Answer/Explanation
Ans: 6.74[0…] cm
Question
Using trigonometry, calculate the value of x.
x = …………………………………………
Answer/Explanation
Ans:
24.9 or 24.925 or 24.9[24…]