5. a roof has an off - centre peak. the short...
5. a roof has an off - centre peak. the shorter side of the roof bc has a length of 13m. the base of the roof measures 5m on the short side of the peak as indicated by dc and 9 metres on the longer side of the roof indicated by ad.\n a. determine the height of the roof, bd, rounded to the nearest whole number. (1/2)\n formula:\n calculations:\n solution with units:\n b. using the height of the roof determine the measure of angle a to the nearest degree. (2)\n formula:\n calculations:\n solution with units:\n financial services & personal budget\n 6. marc received a credit card statement that has an unpaid balance of $1128.32. the interest rate on this credit card is 20.1%. if this balance remains unpaid for 15 days how much simple interest will marc be charged after 15 days? (remember: 365 days/year) (1/2)\n formula:\n calculations:\n solution with units:
Answer
### a. Determine the height of the roof \(BD\)
# Explanation:
## Step1: Apply Pythagorean theorem
Let \(AB = 13m\), \(AD\) be the base - half length and \(BD\) be the height. The base \(AC\) is composed of two parts, assume the base - half length \(AD\) (from the symmetry of the roof) and we know some side - length relationships. Using the Pythagorean theorem in right - triangle \(ABD\), \(AB^{2}=AD^{2}+BD^{2}\). Here, assume the base - half length \(AD = 9m\) and \(AB = 13m\). Then \(BD=\sqrt{AB^{2}-AD^{2}}\).
\[BD=\sqrt{13^{2}-9^{2}}=\sqrt{(13 + 9)(13 - 9)}=\sqrt{22\times4}=\sqrt{88}\approx 9m\]
# Answer:
\(9m\)
### b. Determine the measure of angle \(A\)
# Explanation:
## Step1: Use the tangent function
In right - triangle \(ABD\), \(\tan(A)=\frac{BD}{AD}\). We know from part a that \(BD\approx9m\) and \(AD = 9m\). So \(\tan(A)=\frac{9}{9}=1\).
## Step2: Find the angle
Since \(\tan(A)=1\), and \(A\) is an acute angle in a right - triangle, \(A=\arctan(1)\). Using the inverse - tangent function, \(A = 45^{\circ}\).
# Answer:
\(45^{\circ}\)
### c. Calculate the simple interest
# Explanation:
## Step1: Recall the simple - interest formula
The simple - interest formula is \(I=P\times r\times t\), where \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), and \(t\) is the time in years. Given \(P = 1128.32\), \(r=0.201\), and \(t=\frac{15}{365}\).
## Step2: Substitute the values
\[I = 1128.32\times0.201\times\frac{15}{365}\]
\[I=1128.32\times0.201\times0.041096\]
\[I\approx1128.32\times0.00826\]
\[I\approx9.32\]
# Answer:
\(\$9.32\)